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THEORIES  OF  SOLUTIONS.  By  SVANTE  AUGUST 
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THE  PROBLEMS  OF  GENETICS.  By  WILLIAM  BATE- 
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In  preparation. 


THEORIES  OF  SOLUTIONS 


BY 

SVANTE  ARRHENIUS 

DIRECTOR  OP  THE  NOBEL  INSTITUTE  OF  THE  ROYAL  SWEDISH  ACADEMY 
OF  SCIENCES,  STOCKHOLM 


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MCMXII 


Copyright,  1912 
BY  YALE  UNIVERSITY 

Published  May,  1912 


TO 

JACQUES  LOEB 

IN  ADMIRATION  OF  HIS  APPLICATION  OF 
PHYSICAL  CHEMISTRY  TO  BIOLOGY 


240954 


THE  SILLIMAN  FOUNDATION 

IN  the  year  1883  a  legacy  of  eighty  thousand  dollars  was 
left  to  the  President  and  Fellows  of  Yale  College  in  the 
city  of  New  Haven,  to  be  held  in  trust,  as  a  gift  from  her 
children,  in  memory  of  their  beloved  and  honored  mother 
Mrs.  Hepsa  Ely  Silliman. 

On  this  foundation  Yale  College  was  requested  and 
directed  to  establish  an  annual  course  of  lectures  designed 
to  illustrate  the  presence  and  providence,  the  wisdom  and 
goodness  of  God,  as  manifested  in  the  natural  and  moral 
world.  These  were  to  be  designated  as  the  Mrs.  Hepsa 
Ely  Silliman  Memorial  Lectures.  It  was  the  belief  of  the 
testator  that  any  orderly  presentation  of  the  facts  of  nature 
or  history  contributed  to  the  end  of  this  foundation  more 
effectively  than  any  attempt  to  emphasize  the  elements  of 
doctrine  or  of  creed  ;  and  he  therefore  provided  that  lec- 
tures on  dogmatic  or  polemical  theology  should  be  excluded 
from  the  scope  of  this  foundation,  and  that  the  subjects 
should  be  selected  rather  from  the  domains  of  natural 
science  and  history,  giving  special  prominence  to  astron- 
omy, chemistry,  geology,  and  anatomy. 

It  was  further  directed  that  each  annual  course  should  be 
made  the  basis  of  a  volume  to  form  part  of  a  series  consti- 
tuting a  memorial  to  Mrs.  Silliman.  The  memorial  fund 
came  into  the  possession  of  the  Corporation  of  Yale  Uni- 
versity in  the  year  1902  ;  and  the  present  volume  consti- 
tutes the  eighth  of  the  series  of  memorial  lectures. 


CONTENTS. 


PAGE' 

CONTENTS xi 

INTRODUCTION xvii 

LECTURE  I. 
SHORT  HISTORY  OF  THE  THEORY  OF  SOLUTIONS..      1 

Cosmogonical  ideas  regarding  solutions.  Thales  regarded  water 
as  the  primary  substance.  The  four  elements.  Plato  and  Aristotle. 
The  doctrine  of  transmutation  of  metals.  The  mercury  of  the 
philosophers.  "Osiris."  Views  of  Isaac  Hollandus,  van  Helmont 
and  Boyle.  "Corpora  non  agunt  nisi  soluta"  The  universal 
solvent  "alcahest."  Democritus' atomistic  ideas.  Gassendi  intro- 
duces the  notion  of  atoms  and  molecules.  The  corpuscular  theory 
of  solution.  Nature  of  acids  and  bases.  Contraction  on  mixing. 
Crystal  water.  Newton's  opinions  on  the  solution  phenomenon 
and  the  dissolved  state  of  water.  Buffon's  improvement.  "  Similia 
simihbus  solvuntur  "  Lavoisier  discriminates  between  solution  and 
dissolution.  Liquefaction  and  solution.  Richter  on  deliquescent 
salts.  Berthollet  and  Proust.  Constant  composition  of  salts 
with  crystal  water.  Solution,  a  physical  or  chemical  process?  Ex- 
amples Solutions  from  the  point  of  view  of  the  theory  of  electro- 
lytic dissociation.  Gore's  and  Hittorfs  experiments.  Ionic 
reactions.  Generalization  of  the  ionic  theory.  Goldschmidt's  ex- 
periments regarding  esterification. 

LECTURE  II. 
THE  MODERN  MOLECULAR  THEORY 17 

Application  of  quantitative  measurements  in  chemistry.  The 
constancy  of  mass.  The  work  of  Richter  and  Proust.  Dalton's 
atomic  theory.  The  law  of  multiple  proportions.  The  analytic 
work  of  Berzelius.  Gay-Lussac's  law  of  gas  volumes  and  Avogadro's 
law.  The  kinetic  theory  of  gases.  Wald's  opposition.  Ostwald's 
"  law  of  integral  reactions."  Isomerisms.  The  Brownian  move- 
ment. Investigation  of  Svedberg,  Ehrenhaft  and  Perrin.  The 
number  of  molecules  in  one  grammolecule  is  about  N=69.10».. 

xi 


XU  THEORIES  OF  SOLUTIONS. 

Electric  determinations  of  N.  Other  physical  methods  of  de- 
termining N.  Charge  of  single  droplets.  Planck's  theory  of 
radiant  energy.  Movement  of  molecules  or  ions  according  to 
Svedberg.  Dalton's  repudiation  of  the  laws  of  Gay-Lussac  and 
Avogadro. 

LECTURE  III. 
SUSPENSIONS 36 

Methods  of  preparing  suspensions.  The  size  of  the  suspended 
particles.  Their  rate  of  diffusion.  Their  electric  charge.  Pre- 
cipitation of  suspended  particles.  Their  catalytic  action.  An- 
organic enzymes.  Color  of  suspensions.  Heat  of  suspension. 
Precipitation  of  Raffo's  sulphur. 

LECTURE  IV. 
THE  PHENOMENA  OF  ADSORPTION 55 

Historical  notes.  The  so-called  adsorption-formula.  Influ- 
ence of  temperature.  Schmidt's  discovery  of  a  saturation-point 
for  the  adsorption  of  dissolved  substances.  The  laws  governing 
adsorption-phenomena.  The  work  of  Titoff  and  Miss  Ida  Horn- 
fray.  Points  of  saturation  for  gases.  Heat  of  adsorption,  its 
variation  and  consequences  thereof.  Role  of  the  molecular  attrac- 
tion. Compressibility  of  liquids.  Adsorption  of  albuminous  sub- 
stances. 

LECTURE  V. 

THE   ANALOGY    BETWEEN   THE    GASEOUS   AND    THE 
DISSOLVED  STATE  OF  MATTER 72 

The  development  in  this  fundamental  chapter  is  quite  natural 
and  continuous.  Two  parallel  lines  of  progress,  the  chief  one 
based  on  the  similarity  of  gases  and  dissolved  substances,  the 
other  on  the  application  of  thermodynamics  to  solution.  Newton's 
statement.  Gay-Lussac's  ideas  regarding  the  analogy  between 
evaporation  and  solution.  His  notion  of  equipollency.  Bizio's 
and  Rosenstiehl's  ideas.  Horstmann's  work.  Guldberg  and 
Waage's  law  and  its  development.  Thomsen's  opinion.  Sublim- 
ation and  solution  according  to  the  kinetic  theory  of  gases.  Shen- 
stone's  opinion.  Mendelejew's  ideas  regarding  solutions.  Kirch- 
hoff's  studies  on  vapor  pressure  of  solutions.  Guldberg's  funda- 
mental applications  of  the  thermodynamical  laws  of  solutions. 
The  general  laws  of  solutions  deduced  by  Gibbs.  Helmholtz's 


CONTENTS. 

introduction  of  the  notion  "free  energy."  Le  Chatelier's  law. 
van't  Hoff's  discovery.  The  osmotic  pressure  and  the  work  of 
Traube,  Pfeffer  and  de  Vries.  Planck's  theoretical  deductions. 

LECTURE  VI. 

DEVELOPMENT  OF  THE  THEORY  OF  ELECTROLYTIC 
DISSOCIATION 91 

The  empirical  and  theoretical  ways  leading  to  the  hypothesis 
of  electrolytic  dissociation.  Valson's  investigations  of  additive 
properties.  The  independency  of  the  "elements"  of  dissolved 
substances.  Investigations  by  Kohlrausch,  Gladstone,  G.  Wiede- 
mann,  Oudemans,  Landolt  and  Hess.  Rontgen's  and  Schneider's 
measurements.  Raoult's  work  on  freezing  points.  Opposition 
of  E.  Wiedemann.  Williamson's  theory.  Grotthuss'  chains. 
Clausius'  deductions  from  the  kinetic  theory.  Bartoli's  ideas. 
Active  and  inactive  molecules.  Parallelism  between  electric  and 
chemical  activity.  Reactions  of  ions.  Ostwald's  measurement 
of  the  activity  of  acids.  The  law  of  change  of  conductivity  with 
dilution. 

LECTURE  VII. 
VELOCITY  OF  REACTIONS 112 

Inversion  of  cane  sugar  studied  by  Wilhelmy  1850.  Law  of 
monomolecular  reactions.  Action  of  catalytic  agents  of  inorganic 
nature,  of  enzymes,  of  high  temperature  and  of  ultraviolet  light. 
Action  of  invertase.  Hudson  versus  Henri.  Action  of  zymase 
and  analogous  processes.  Digestion  process.  Action  of  chloro- 
phyll. Accelerating  substances.  Growth  of  bacteria.  Retarding 
processes.  Schuetz's  rule.  Formation  of  ether  according  to  Kre- 
mann.  Radioactive  processes.  Dissolution  in  acids.  Photochem- 
ical reactions.  Decomposition  of  HI.  Spontaneous  decomposition 
of  ferments.  Concomitant  processes.  Influence  of  temperature. 
Van't  Hoff's  rule. 

LECTURE  Vm. 

CONDUCTIVITY  OF  SOLUTIONS  OF  STRONG  ELECTRO- 
LYTES   131 

Kirchhoff's,  Guldberg's  and  Horstmann's  theoretical  investiga- 
tions. The  work  of  Berthelot  and  P6an  de  St.  Gilles.  Equilibria. 
Strong  electrolytes.  Van't  Hoff's  equation.  Migration  numbers 
of  Hittorf.  Influence  of  temperature.  Noyes'  work.  Alcoholic 
solutions.  Godlewski's  determinations.  Peculiarity  of  H-  and 


XIV  THEORIES  OF  SOLUTIONS. 

OH-ions.  Influence  of  fluidity.  Different  influence  on  different 
groups  of  salts.  Organic  solvents.  Influence  of  temperature. 
Fused  salts.  Abnormal  behavior  of  electrolytes  on  dilution. 
Foote's  and  Martin's,  Walden's  and  Franklin's  measurements. 
Lorenz  on  fused  salts.  Carrara's  opinion. 

LECTURE  IX. 
EQUILIBRIA  IN  SOLUTIONS 153 

Henry's  law.  Investigations  of  Berthelot  and  Jungfleisch  and 
by  Nernst.  Moore  on  equilibrium  in  ammoniacal  solutions. 
Red  blood-corpuscles  and  bacteria.  Amphoteric  electrolytes, 
investigations  by  Bredig  and  Winkelblech,  Walker  and  Lunde*n. 
The  laws  of  diffusion.  Nernst's  theory.  Salt  action.  Guldberg 
and  Waage's  opinion.  Weakening  of  acids  by  their  salts.  Avidity. 
Hydrolysis.  Pseudo-acids  and  pseudo-bases  of  Hantzsch.  Wake- 
man  and  Godlewski  on  solutions  in  mixed  alcohol  and  water. 
Work  of  Kahlenberg.  Van't  Hofif's  opinion. 

LECTURE  X. 
THE  ABNORMALITY  OF  STRONG  ELECTROLYTES 172 

Different  ways  of  explaining  Jahn's  opinion.  The  electro- 
static influence.  The  hydration  theory.  Hydration  of  ions. 
Saturation.  Specific  weight  of  salt  solutions.  Expansion  on 
neutralization.  Electrostriction.  Bousfield's  and  Riesenfeld's  cal- 
culations. Washburn's  method.  Correction  of  Hittorf's  figures. 
Explanation  of  the  data.  Mobility  of  organic  ions  according  to 
Bredig.  Influence  of  variable  hydration  on  molecular  conductiv- 
ity. 

LECTURE  XI. 

THE  DOCTRINE  OF  ENERGY  IN  REGARD  TO  SOLU- 
TIONS   196 

Free  energy  of  dissolved  substances  and  of  gases.  Heat  evolved 
at  solution  or  electrolytic  dissociation.  Hypothesis  regarding 
the  possibility  of  developing  the  expression  for  the  free  energy 
in  a  series.  Discussion  of  formulae.  Study  of  the  solution 
phenomenon.  Pairs  of  non-miscible  liquids.  Heats  of  solution. 
Influence  of  dissociation.  Change  of  energy  at  electrolytic  dis- 


CONTENTS.  XV 

sociation.  Noye's  determinations.  Compression  with  evapora- 
tion. Influence  of  change  of  units.  General  results  from  Lunde*n's 
figures.  The  free  energy  is  better  adapted  to  chemical  calculations 
than  the  evolution  of  heat. 

BIBLIOGRAPHICAL  REFERENCES..  .  226 

INDEX  OF  AUTHORS 239 

INDEX  OF  SUBJECTS. .  .  243 


INTRODUCTION. 

IT  is  an  exquisite  honor  to  speak  from  this  platform 
in  this  celebrated  university  where  Willard  Gibbs  enun- 
ciated his  standard  work  on  "the  theory  of  heteroge- 
neous equilibria. ' '  I  also  feel  very  much  indebted  for  the 
invitation  to  give  a  series  of  Silliman  lectures,  which 
have  been  delivered  by  the  most  prominent  men  of 
the  scientific  world.  I  therefore  extend  to  you  my 
warmest  thanks  for  having  conferred  this  rare  distinc- 
tion upon  me. 

The  object  of  my  lectures  will  be  some  chapters  of 
modern  physical  chemistry.  This  branch  of  science 
has  been  treated  in  a  rather  great  number  of  good  or 
even  excellent  text-books,  here  as  well  as  in  Europe. 
It  is  therefore  a  difficult  task  to  give  something  new 
and  something  which  has  not  already  before  been 
worked  out  in  a  masterly  manner.  But  it  seems  to 
me  as  imprudent  as  to  carry  owls  to  Athens  to  give 
you  a  course  of  physical  chemistry  as  it  is  presented  in 
the  text-books.  Therefore  I  have  confined  myself  to 
some  problems  which  are  now  under  debate  and  which 
are  still  not  finished  but  which  promise  the  greatest 
interest  for  further  investigations.  Also  when  I  refer 
to  older  investigations,  I  try  to  exhibit  such  facts  as 
have  not  in  a  higher  degree  attracted  the  attention  of 
the  authors  of  text-books  in  this  branch,  and  thereby 
to  give  a  broader  and  more  complete  view  of  the  excep- 
tionaly  fertile  field  which  we  cultivate.  I  have  often 

xvii 


XV111  THEORIES  OF  SOLUTIONS. 

found  it  useful  to  drag  old  historical  data  into  the 
light  especially  in  order  to  give  an  idea  of  the  strict 
harmonical  development  of  this  subject,  a  circumstance 
which  is  often  forgotten  even  to  such  a  degree  that 
physical  chemistry  is  generally  represented  as  if  it  had 
like  Minerva  sprung  out  quite  fully  developed  from 
Jupiter's  head. 

What  I  wish  to  express  to  you  is  therefore  something 
which  according  to  my  opinion  supplements  the  excel- 
lent text-books  which  you  already  have  perused.  It  is 
of  course  agreeable  to  me  to  lay  before  you  my  personal 
individual  ideas.  On  the  other  hand  it  is  quite  clear 
that  it  would  be  a  great  mistake  if  my  attempt  were 
understood  to  be  designed  to  embrace  all  the  branches 
or  even  the  most  important  branches  of  modern 
physical  chemistry.  But  I  feel  quite  sure  that  such 
an  intelligent  auditory  as  that  to  which  I  have  the 
honor  of  speaking  here  will  not  commit  this  mistake 
and  I  trust  the  lacunae  of  my  exposition  will  be  easily 
filled  up  by  you  who  have  been  introduced  so  thoroughly 
into  the  different  chapters  of  physical  chemistry  by 
your  excellent  scientific  leaders  and  by  the  unrivalled 
interest  which  the  enlightened  scientific  opinion  here 
in  America  even  more  than  in  the  old  world  attaches 
to  this  wonderful  branch  which  is  called  physical 
chemistry  and  which  is  of  the  greatest  use  not  only  for 
the  most  important  doctrines  of  the  natural  sciences 
and  medicine  but  also  for  its  far-reaching  applications 
to  modern  industry.  There  are  very  few  doctrines  in 
exact  science  where  so  few  lecture  experiments  are 
shown  as  in  physical  chemistry.  This  depends  upon 
its  theoretical  character.  The  methods  of  working  are 


INTRODUCTION.  XIX 

taken  from  the  science  of  physics.  There  is  almost 
only  one  chapter,  which  is  so  to  say  specially  adapted 
for  lecture  experiments  in  physical  chemistry,  namely, 
that  regarding  catalytic  action.  For  this  chapter,  a 
number  of  demonstrative  experiments  are  worked  out 
by  Professor  A.  A.  Noyes  and  G.  V.  Sammet  in  Boston. 
Another  number  of  good  lecture  experiments  are  de- 
scribed in  a  little  book  by  Professor  Emil  Baur  in 
Braunschweig.  It  may  suffice  to  draw  attention  to 
these  expositions  of  the  relatively  small  prominence  of 
the  experimental  part  of  our  science.  The  great  progress 
in  physical  chemistry  depends  upon  the  quantitative 
measurements  on  which  the  general  laws  are  based. 
In  most  cases  it  has  been  necessary  to  collect  the 
evidence  from  a  very  vast  field  and  an  extraordinarily 
great  number  of  experiments  in  order  to  get  a  view  of 
the  real  situation  of  the  problems  and  of  the  possibility 
of  solving  them.  Chemistry  works  with  an  enormous 
number  of  substances,  but  cares  only  for  some  few  of 
their  properties;  it  is  an  extensive  science.  Physics  on 
the  other  hand  works  with  rather  few  substances,  such 
as  mercury,  water,  alcohol,  glass,  air,  but  analyses  the 
experimental  results  very  thoroughly;  it  is  an  intensive 
science.  Physical  chemistry  is  the  child  of  these  two 
sciences;  it  has  inherited  the  extensive  character  from 
chemistry.  Upon  this  depends  its  all-embracing  fea- 
ture, which  has  attracted  so  great  admiration.  But 
on  the  other  hand  it  has  its  profound  quantitative  char- 
acter from  the  science  of  physics.  From  this  circum- 
stance the  great  solidity  and  strength  of  our  science 
is  derived.  The  results  of  these  quantitative  measure- 
ments regarding  the  properties  of  a  very  great  number  of 


XX  THEORIES  OF   SOLUTIONS. 

substances  is  very  difficult  to  present  by  lecture  experi- 
ments; they  must  be  given  in  diagrams  and  tables. 
I  feel  it  necessary  to  explain  from  the  very  begin- 
ning why  I  have  preferred  to  give  a  series  of  theoretical 
lectures  rather  than  of  experimental  ones;  the  cause 
lies  in  the  very  character  of  the  modern  development 
of  our  science.  Therefore  modern  physical  chemistry 
is  often  called  general  or  theoretical  chemistry  as  in 
the  two  excellent  German  text-books  of  Ostwald  and 
Nernst. 

The  theoretical  side  of  physical  chemistry  is  and  will 
probably  remain  the  dominant  one;  it  is  by  this  peculiar- 
ity that  it  has  exerted  such  a  great  influence  upon  the 
neighboring  sciences,  pure  and  applied,  and  on  this 
ground  physical  chemistry  may  be  regarded  as  an 
excellent  school  of  exact  reasoning  for  all  students  of 
natural  sciences. 


LECTURE  I. 

SHORT  HISTORY  OF  THE  THEORY  OF  SOLUTIONS. 

IP  we  go  very  far  back  into  antiquity  we  find  how 
our  modern  chemical  ideas  slowly  crystallised  out  from 
limited  experiences  and  a  naive  attempt  at  generaliza- 
tion. It  is  very  interesting  to  find  how  solutions,  which 
are  now  the  chief  material  agent  of  the  chemist,  even 
at  that  time  attracted  the  main  attention.  In  a  great 
number  of  the  cosmogonic  myths  the  world  is  said  to 
have  developed  from  a  great  water,  which  was  the 
prime  matter.  In  many  cases,  as  for  instance  in  an 
Indian  myth,  this  prime  matter  is  indicated  as  a  solu- 
tion, out  of  which  the  solid  earth  crystallized  out. 

Later  on  we  find  that  Thales  (624-523  B.C.)  describes 
water  as  the  origin  of  everything.  Probably  Thales 
had  taken  up  this  doctrine  from  ancient  Egypt,  which 
is  according  to  all  probability  the  country  where  the 
first  very  modest  development  of  our  science  took  place. 
Certainly  the  idea  of  the  four  primary  elements,  which 
is  generally  attributed  to  its  prominent  advocate  the 
Greek  philosopher,  Empedocles  (500  B.C.),  is  also  of 
Egyptian  origin.  There  are  philosophers  who  regard 
one  of  the  elements  as  the  chief  one,  for  instance  Thales 
water,  Anaximenes  air,  Heraclitus  fire  and  Xenophanes 
earth,  but  water  is  generally  preferred.  Empedocles 
taught  the  doctrine  of  the  transmutability  of  the  four 
elements,  that  they  were  in  a  certain  sense  equivalent. 

The  doctrine  of  Empedocles  was  taken  up  by  the 


2  THEORIES   OF   SOLUTIONS. 

philosophers  Plato  and  Aristotle  whose  ideas  dominated 
the  methods  of  reasoning  until  two  hundred  years  ago 
and  who  still  exert  a  great  influence  in  the  philosophical 
sciences.  In  Plato's  work  Timaios  we  read:  "We 
believe  from  observation  that  water  becomes  stone  and 
earth  by  condensation,  and  wind  and  air  by  subdivision; 
ignited  air  becomes  fire,  but  this  when  condensed  and 
extinguished,  again  takes  the  form  of  air,  and  the  latter 
is  then  transformed  to  mist,  which  coalesces  into  water. 
Lastly  rocks  and  earth  are  produced  from  water." 
Evidently  the  four  elements  of  antiquity  correspond 
nearly  with  what  we  now  call  states  of  aggregation. 
The  ancients  had  observed  the  transformation  of  water 
into  steam  and  vice  versa,  this  phenomenon  as  well  as 
the  deposition  of  solid  substances  from  solutions  or 
suspensions  in  water  was  the  chief  one  upon  which  they 
built  their  theory.  Under  all  circumstances  water  was 
the  chief  material  from  which  they  gained  then-  experi- 
ence. 

In  antiquity  the  chief  products  of  industrial  chem- 
istry were  the  metals.  Plato  and  especially  Aristotle 
developed  the  idea  of  transmutation  of  the  metals. 
Even  in  this  department  the  condition  of  fluidity  seemed 
to  be  most  valuable  for  the  reactions  and  therefore  the 
fluid  metal,  mercury,  attracted  the  attention  of  the 
chemists  more  than  the  other  metals  did.  It  tinged  the 
metals  generally  silver-white  and  was  supposed  to  be 
the  prime  matter  of  all  metals.  This  prime  matter  was 
called  the  " mercury  of  the  philosophers"  and  regarded 
as  the  " ghost"  of  the  metals,  which  was  the  bearer  of 
the  metallic  properties.  In  Egypt  lead  seems  to  have 
played  a  similar  role  and  therefore  received  the  name 


HISTORY   OF   THE   THEORY   OF   SOLUTIONS.  3 

of  " Osiris"  from  the  principal  deity  of  the  old  Egyp- 
tians. A  rather  moderate  heat  is  sufficient  for  convert- 
ing lead  into  the  liquid  state,  in  which  it  acts  as  a 
solvent  on  other  metals.  Olympiodoros  says  "  Osiris  is 
the  principle  of  everything  liquid,  it  is  Osiris,  which 
causes  the  condensation  in  the  sphere  of  fire."  Under 
the  name  of  lead  or  " Osiris"  also  tin  "the  white  lead" 
in  contradistinction  to  the  common  or  " black  lead" 
was  included.  In  many  minerals  from  which  lead  was 
extracted  a  small  quantity  of  silver  is  contained.  This 
could  easily  be  separated  from  the  lead  and  as  the 
silver  was  more  valuable  it  was  regarded  as  "the  perfect 
lead."  These  considerations  are  quite  characteristic 
of  the  reasoning  of  the  alchemists.  When  mercury  was 
discovered,  about  the  tune  of  the  Peloponnesian  war,  it 
was  found  much  more  satisfactory  for  dissolving  and 
tinging  metals  than  lead  and  was  therefore  supposed  to 
be  the  "materia  prima."  The  readiness  with  which  it 
could  by  evaporation  be  separated  from  other  metals 
made  the  experiments  with  mercury  much  easier  than 
those  with  lead. 

The  liquid  state  was  already  at  that  time  found  to  be 
the  most  suitable  condition  for  chemical  reactions. 
The  chemistry  of  the  Middle  Ages  up  to  the  seventeenth 
century  retained  the  same  view.  In  the  writings  of 
Isaac  Hollandus  (at  the  beginning  of  the  15th  century) 
we  read  that  "the  philosophers  have  followed  the 
direction  given  by  Nature  and  at  first  transformed 
everything  to  water"  (i.  e.,  dissolved  it)  "before  they 
used  it  in  the  art  of  chemistry."  According  to  van 
Helmont  (1577-1644),  the  greatest  chemist  of  his  time, 
and  the  discoverer  of  carbonic  acid  (gas  sylvestre), 


4  THEORIES   OF   SOLUTIONS. 

"water  is  the  primary  element,  into  which  all  substances 
may  be  reduced."  Boyle,  the  father  of  modern 
chemistry  (1626-1691)  opposed  the  ideas  of  Aristotle 
and  his  alchemical  successors  regarding  the  four  ele- 
ments; he  expressed  the  opinion  that  only  such  sub- 
stances should  be  called  elements,  which  are  undecom- 
posable  constituents  of  matter,  but  in  his  "  Sceptical 
chymist"  he  still  expresses  the  opinion  that  water  may 
be  transmuted  into  all  other  elements." 

The  experience  of  the  alchemists  was  summed  up 
under  the  formula  "the  Substances  do  not  act  upon 
each  other  unless  they  are  dissolved  "  (corpora  non  agunt 
nisi  soluta)  or  that  the  salts  do  not  give  any  reaction, 
if  not  dissolved,  and  then  not  too  much  diluted  (Salia 
non  agunt  nisi  dissoluta,  nee  agunt  si  dissoluta  nimis) . 
This  last  part  of  the  sentence  evidently  refers  to  the 
circumstance  that  precipitations,  which  are  often 
observed  after  mixing  solutions  of  two  different  salts, 
do  not  occur,  if  the  solutions  are  too  dilute,  so  that 
the  liquid  retains  the  newly  formed  salts  in  unsaturated 
solution.  Van't  Hoff  and  Le  Chatelier  find  also  that 
reactions  proceed  much  more  regularly,  when  the 
reacting  substances  are  dissolved,  than  if  they  are  not. 

As  the  solubility  of  a  substance  was  regarded  as 
the  necessary  condition  for  its  entering  into  chemical 
reactions,  the  great  problem  of  chemistry  was  to  find 
a  solvent  for  all  possible  substances.  This  hypothetical 
solvent  was  called  "alcahest"  by  Paracelsus  (1493- 
1541).  The  alcahest  was  regarded  as  "the  stone  of 
the  wise"  or  as  the  "life-elixir"  and  very  many  receipts 
for  its  preparation  were  given.  Kunckel  (1716)  gives 
a  very  satirical  and  severe  criticism  of  these  receipts, 


HISTORY   OF   THE   THEORY   OF   SOLUTIONS.  5 

when  he  says  that  the  great  problem  was  to  find  a 
vessel  which  would  not  be  dissolved  by  the  alcahestic 
liquid,  otherwise  there  would  be  no  possibility  of 
using  it. 

The  most  celebrated  natural  philosopher  of  antiq- 
uity was  Democritus  of  Abdera  (born  460  B.C.). 
He  had  proposed  an  atomic  theory,  according  to 
which  matter  consists  of  discrete  atoms  with  empty 
interstices.  Plato  taught  that  the  molecules  of  one 
substance  might  enter  into  the  interstices  between  the 
atoms  of  another  substance.  Aristotle  opposed  the 
atomic  doctrine.  Through  his  great  authority  the  revivi- 
fication of  the  atomic  theory  was  hindered  until  Gas- 
sendi  (1592-1655)  took  up  and  elaborated  the  ideas  of 
Democritus.  According  to  Gassendi  a  number  of  atoms 
could  unite  to  form  molecules.  Solution  depends  then 
upon  the  particles  of  the  substance,  which  goes  into 
solution,  entering  into  the  pores  of  the  solvent.  As  the 
particles  of  common  salt  were  regarded  as  small  cubes 
according  to  the  crystal  form  of  this  substance,  it 
was  said  that  this  salt  filled  up  the  pores  of  cubical 
form  between  the  water-particles.  If  all  the  cubical 
pores  were  so  filled  up,  the  salt-solution  was  saturated 
and  could  not  dissolve  more  salt.  It  was  known  that 
other  salts,  e.  g.t  the  octahedral  alum,  might  be  taken  up 
by  the  said  solution.  Therefore  it  was  supposed  that 
the  water  contains  other  pores  of  octahedral  form,  into 
which  the  alum  but  not  the  common  salt  could  enter. 

This  so-called  corpuscular  theory  was  used  by  Boyle 
in  his  investigations  and  won  through  this  circumstance 
a  great  credence.  It  was  propagated  in  the  highest 
degree  by  Le*mery's  "Cours  de  Chimie,"  the  most-used 


6  THEORIES  OF  SOLUTIONS. 

text-book  on  chemistry  at  that  time  (first  ed.  1675,  last 
1756).  In  order  to  explain  the  capacity  of  acids  to  act 
as  solvents  for  metals  it  was  supposed  that  the  particles 
of  the  acid  were  very  sharp  and  pointed,  so  that  they 
entered  easily  between  the  particles  of  the  metals  and 
tore  them  from  each  other  by  their  violent  motion.  This 
acute  angulated  form  of  the  acid  particles  was  also 
evident  from  the  shape  of  their  crystals,  which  was 
described  as  acicular,  as  well  as  from  their  sharp  taste. 
The  alkalis  were  supposed  to  possess  pores  in  which  the 
points  of  the  acid  particles  were  broken  off,  so  that  the 
acid  lost  its  solvent,  properties  and  a  salt  resulted. 
Reaumur  explained  in  a  similar  manner  the  fact  that 
a  contraction  takes  place  if  alcohol  is  dissolved  in  water. 
It  was  also  supposed  by  Reaumur  that  water  could 
fill  up  the  pores  between  the  particles  of  crystals,  e.  g., 
of  sulphuric  acid;  this  is  the  first  tune  that  the  idea  of 
water  of  crystallization  is  mentioned. 

It  is  clear  that  this  theory  of  solution  could  not  be 
satisfactory.  It  was  necessary  to  suppose  all  possible 
kinds  of  interstices  in  the  different  solvents  and  the 
widely  varying  solvent  power  of  different  solvents  found 
no  explanation.  At  that  time  Newton's  great  discoveries 
were  evoking  the  admiration  of  the  scientific  world. 
Newton  himself  supposed  that  the  universal  force,  acting 
between  the  celestial  bodies,  was  also  able  to  bind 
together  two  different  substances  and  cause  their  union 
to  a  new  system.  He  maintained  that  a  salt  is  dissolved 
by  water  if  its  particles  exert  a  greater  attraction  on 
water-molecules,  than  on  each  other.  This  doctrine 
was  accepted  by  the  founder  of  the  phlogiston-theory, 
Stahl,  and  in  general  by  the  scientific  world  and  is  in 


HISTORY  OF  THE   THEORY  OF  SOLUTIONS.  7 

a  certain  sense  prevalent  at  the  present  time,  although 
we  do  not  suppose  that  the  chemical  forces  are  of  the 
same  nature  as  that  of  gravitation.  Very  interesting 
is  another  statement  by  Newton  namely  that  the  dis- 
solved molecules  tend  to  get  away  from  each  other  as 
if  they  were  gifted  with  a  repulsive  force  against  each 
other.  This  view  reminds  one  very  much  of  the 
modern  theory  of  osmotic  pressure  which  is  regarded 
as  analogous  to  the  pressure  of  a  gas.  So-called  affi- 
nity-tables were  now  constructed  in  which  was  tabu- 
lated the  extent  to  which  a  certain  substance  is  soluble 
in  a  given  solvent.  But  even  at  an  early  stage  it  was 
found  difficult  to  maintain  the  parallel  between  affinity 
and  gravitation.  This  latter  force  is  independent 
of  the  other  properties  of  the  attracting  substances  and 
determined  only  by  their  mass,  whereas  the  solubility 
is  in  the  highest  degree  dependent  on  the  kind  of 
matter  contained  in  the  solvent  and  solute.  Buffon 
therefore  added  to  the  Newtonian  hypothesis  a  secon- 
dary one,  according  to  which  the  form  of  the  molecules 
was  of  very  great  importance  in  the  phenomenon  of 
solution,  where  the  molecules  come  into  the  very  closest 
contact  with  each  other,  whereas  in  the  case  of  gravita- 
tion the  molecules  of  the  two  acting  bodies  lie  at  such 
great  distances  from  each  other  that  then*  form  is  of 
no  importance. 

This  idea  was  accepted  with  great  approval  by  the 
leading  chemists.  It  was  found  as  a  general  rule  that 
a  certain  similarity  prevails  between  two  substances 
which  mix  with  each  other  in  a  solution  (similia 
similibus  solvuntur),  and  this  rule  has  retained  its  value 
until  the  present  day. 


8  THEORIES   OF   SOLUTIONS. 

It  was  also  evident  that  the  solution  of  a  salt  or  of 
cane  sugar  in  water  is  a  process  of  a  very  mild  kind,  for 
it  is  possible  to  separate  the  solvent  from  the  dissolved 
body  by  simple  distillation.  The  solution  of  a  metal 
in  an  acid  on  the  other  hand  gives  a  chemical  change 
of  a  much  more  deeply  seated  nature,  a  salt  is  formed, 
which  differs  totally  from  both  the  metal  and  the  salt, 
and  it  is  generally  very  difficult  to  recover  either  the 
metal  or  the  acid  from  the  salt.  Lavoisier  therefore 
called  this  latter  process  dissolution  in  contradistinction 
to  simple  solution.  Upon  dissolution  a  real  chemical 
decomposition  of  the  solvent  and  the  solute  takes  place. 
On  the  other  hand  the  process  of  solution  consists 
according  to  Lavoisier  simply  in  a  separation  of  the 
molecules  of  the  dissolved  substance,  which  suffers  no 
real  chemical  change. 

Lavoisier  directed  attention  to  another  circumstance. 
He  reasoned  in  the  following  manner.  If  I  heat  a  salt 
to  a  sufficiently  high  temperature  it  becomes  liquefied, 
just  as  by  the  use  of  a  solvent.  It  seems  obvious  from 
this  circumstance,  that  if  heat  and  a  solvent  are  applied 
simultaneously  to  the  salt  their  concurrent  action  will 
be  greater  than  that  of  either  alone.  In  other  words 
the  solubility  should  increase  with  temperature.  This 
corresponds  very  well  with  the  facts  of  every-day  expe- 
rience, and  was  a  familiar  fact  to  the  alchemists.  For 
Lavoisier  the  conclusion  seemed  still  more  evident  as 
heat  at  that  time  was  regarded  as  a  form  of  matter 
("caloric")  analogous  to  the  solvent  water,  although 
of  a  finer  kind.  It  was  not  known  by  him  that  some 
substances  diminish  in  solubility  with  increasing  tem- 
perature. Even  liquefaction  is  not  perfectly  analogous 


HISTORY   OF   THE   THEORY   OF   SOLUTIONS.  9 

to  solution,  otherwise  one  would  expect  that  two  liquids 
would  mix  in  any  proportions,  which  is  certainly  the 
case  with  many  pairs  of  liquids  such  as  alcohol  and 
water,  but  is  not  so  with  many  others,  for  instance  oil 
and  water,  a  fact  which  was  very  well  known  from  the 
earliest  times. 

The  ideas  of  Lavoisier  were  not  accepted  by  the 
majority  of  the  alchemists  at  that  time.  Richter  (1793) 
is  of  the  opinion  that  a  certain  affinity  causes  solution. 
Thus  for  instance  he  says  that  it  is  possible  to  precipi- 
tate salts  from  their  solutions  in  water  by  adding  some 
substance,  such  as  alcohol,  which  has  a  greater  affinity 
for  water  than  the  salt  has.  In  the  same  manner,  he 
says,  a  deliquescent  salt  takes  up  water  from  the  air  and 
gives  a  solution,  "  because  the  salt  has  a  greater  affinity 
for  water,  than  the  air  has."  These  examples  especially 
the  latter  one,  indicate  that  his  views  do  not  stand  very 
severe  criticism. 

The  same  is  the  case  with  the  renowned  physico- 
chemist  Berthollet.  He  was  of  the  opinion  that  the 
components  of  chemical  compounds  do  not  enter  into 
them  in  constant  proportions  and  that  solutions  are 
typical  chemical  compounds  of  variable  proportions. 
He  observed  that  if  mercury-sulphate  is  dissolved  in 
water  real  chemical  changes  take  place  and  he  believed 
that  these  changes  do  not  occur  according  to  constant 
proportions.  There  is  in  his  opinion  only  a  difference 
of  degree  between  a  solution  and  a  very  well  defined 
chemical  compound.  Hence  he  was  induced  to  deny 
the  law  of  constant  proportions  in  chemical  compounds. 
It  is  well  known  that  he  was  defeated  in  the  battle 
with  Proust  on  this  point.  Proust  conceded  that  water 


10  THEORIES   OF   SOLUTIONS. 

might  enter  into  combination  with  certain  substances, 
e.  g.,  salts.  These  compounds  are  known  in  the 
crystalline  state  under  the  name  of  crystal  hydrates. 
They,  as  well  as  other  chemical  compounds,  are  char- 
acterized by  their  constant  composition.  (Later  on  it 
has  been  found  by  Mallard  and  Klein  that  the  zeoliths 
may  lose  a  part  of  their  crystal  water  without  changing 
then-  form  of  crystallisation;  other  examples  of  similar 
kind  are  given  by  Tammann  and  by  Loewenstein). 

Berthollet  argued  that  not  only  the  solution  of  solid 
or  liquid  substances  in  liquids  but  even  the  solution  of 
gases  in  liquids  is  due  to  a  chemical  process.  In  this 
latter  case  the  dissolved  quantity  of  the  gas  is  dependent 
on  the  pressure  of  the  gas  and  for  weak  solutions  simply 
proportional  to  that  pressure.  Of  course  it  is  possible 
to  suppose  that  in  this  case  an  attraction  takes  place 
between  the  dissolved  gas-molecules  and  the  solvent. 
But  if  as  for  instance  with  oxygen,  hydrogen  or  nitrogen 
in  water  the  concentration  of  the  gas-molecules  is  less 
in  the  solution  than  hi  the  gas  above  (which  also 
contains  some  molecules  of  gaseous  water),  it  will  be 
necessary  to  suppose  that  the  attraction  of  the  gas- 
molecules  to  the  fluid  water  is  less  than  that  to  the 
sparingly  distributed  water-molecules  in  the  gas-phase, 
an  absolutely  untenable  idea. 

From  this  time  dates  the  still  actual  discussion 
whether  solution  is  a  physical  or  chemical  process. 
Even  at  that  time  it  was  considered  that  the  contraction 
or  the  heat  effect  usually  observed  when  a  substance  is 
dissolved  or  its  solution  diluted,  is  a  certain  indication 
of  a  chemical  process.  On  the  same  ground  it  would 
be  right  to  suppose  that  similar  phenomena  observed  at 


HISTORY  OF  THE   THEORY  OF  SOLUTIONS.  11 

the  freezing  of  a  liquid  indicate  that  freezing  is  a 
chemical  process.  Berthollet  seems  also  to  have  held 
this  opinion.  But  the  majority  of  scientists  regard 
solidification  as  a  physical  process.  On  the  other  hand 
it  must  be  conceded  that  this  process  is  of  absolutely 
the  same  nature  as  the  conversion  of  one  allotropic 
modification  of  a  substance  into  another,  for  instance 
monoclinic  sulphur  into  rhombic  sulphur.  In  reality 
there  is  no  sharp  limit  between  physical  and  chemical 
processes.  The  best  definition  to  decide  between  a 
physical  and  a  chemical  process  is  the  following:  In  a 
physical  process  the  molecules  of  the  acting  substances 
undergo  no  change,  in  a  chemical  process  a  change  of 
the  molecular  structure  occurs.  In  many  cases  the 
change  is  extremely  insignificant  and  then  the  decision 
is  difficult.  For  instance  the  abnormal  behaviour  of 
water,  in  showing  a  maximum  of  density  at  about  4°  C. 
is  certainly  due  to  the  presence  in  the  water  of  two  kinds 
of  water-molecules,  the  water-molecules  proper  and  the 
ice-molecules,  which  are  in  chemical  equilibrium. 
With  lowering  of  the  temperature  this  equilibrium  is 
changed,  some  of  the  water-molecules  proper  are  trans- 
formed into  ice-molecules.  Thereby  the  volume  in- 
creases just  as  when  water  freezes  to  ice.  Of  course  the 
ice-molecule  has  another  structure  (probably  more 
complex)  from  that  of  the  water-molecule.  It  would 
therefore  be  right  to  say  that  on  cooling  water  below 
4°  C.  a  chemical  process  takes  place.  But  the  prop- 
erties of  the  water  change  so  very  little  in  this  process 
that  most  people  agree  to  call  it  a  physical  process. 
In  reality  it  is  a  combination  of  a  physical  and  a 
chemical  process.  The  ice-molecules  as  well  as  by  far 


12  THEORIES   OF   SOLUTIONS. 

the  greater  number  of  the  water-molecules  remain 
unchanged  when  the  temperature  is  lowered  between 
+  4°  C.  and  0°.  These  molecules  are  therefore  only 
subject  to  physical  processes.  Probably  a  very  small 
number  of  the  water-molecules  undergo  a  change  of 
structure  so  that  they  are  transformed  into  ice-mole- 
cules. These  molecules  are  obviously  subject  to  a 
real  chemical  change.  But  this  process  is  rather  un- 
important and  is  therefore  mostly  neglected. 

In  the  same  manner  if  we  have  acetic  acid,  say  in  1 
per  cent,  solution,  the  dissociation  theory  says  that 
about  one  per  cent,  of  the  CH3COOH  molecules  are 
(at  25°  C.)  decomposed  into  their  ions  CH3COO  and 
H.  If  we  dilute  this  solution  to  double  its  volume  with 
water,  the  number  of  the  dissociated  molecules  increases 
in  the  proportion  1.41  to  1  at  the  expense  of  the  undis- 
sociated  molecules.  The  98.6  per  cent,  of  undissociated 
molecules  remain  unchanged,  only  0.4  per  cent,  of  them 
being  split  up  into  their  ions  on  dilution.  In  this  case 
the  chief  process  is  certainly  only  a  physical  one,  and 
most  scientists  therefore  agree  in  regarding  the  whole 
Drocess  as  a  physical  one  although  0.4  per  cent,  of  the 
acetic  acid  molecules  undergo  a  rather  important 
change  of  structure.  Perhaps  in  this  case  also  a  very 
slight  hydration  takes  place,  which  must  be  regarded 
as  a  chemical  change — an  addition  of  water  to  the  acetic 
acid  molecule,  but  such  a  process  is  about  of  the 
same  degree  of  insignificance  as  the  transformation  of 
water-molecules  to  ice-molecules.  It  is  therefore  no 
wonder  that  it  is  regarded  as  a  physical  one,  although 
some  very  slight  chemical  change  occurs  at  the  same 
time.  On  the  other  hand  the  transformation  of  water 


HISTORY   OF   THE   THEORY   OF   SOLUTIONS.  13 

into  ice  is  probably  mainly  a  chemical  process,  because 
in  the  water  at  0°  C.  the  overwhelming  proportion  of 
the  molecules  is  of  the  water-molecule  kind  and  only 
very  few  ice-molecules  occur.  All  those  are  at  the 
congelation  transformed  into  ice-molecules,  a  chemical 
process.  Therefore  the  freezing  of  water  should  prop- 
erly be  regarded  as  in  the  main  a  chemical  process. 
Most  scientists  say  that  it  is  a  physical  one.  Such 
an  assertion  is  connected  with  the  ease  with  which  it  is 
carried  out  in  the  direction  from  water  to  ice,  as  well  as 
in  the  opposite  direction  from  ice  to  water.  If  we  do 
not  take  the  very  unstable  super-cooled  water  into 
consideration,  the  two  modifications  of  water,  namely 
fluid  water  and  ice  do  not  exist  both  together  at  any  tem- 
perature except  0°  C.  (at  ordinary  pressure),  and  if  an 
ice-crystal  is  brought  into  contact  with  the  supercooled 
water  the  latter  very  rapidly  freezes  to  ice  with  an 
elevation  of  the  temperature  to  0°  C.  On  the  other 
hand  the  transformation  of  rhombic  sulphur  into 
monoclinic  or  inversely  takes  place  very  slowly  even 
in  the  presence  of  the  modification  stable  at  the 
temperature  under  consideration.  Still  more  is  this 
the  case  with  common  and  grey  tin.  The  latter  is 
stable  below  18°,  as  Cohen  has  shown,  but  is  very 
rarely  found.  On  common  tin  which  has  been  in- 
oculated with  it,  it  grows  slowly  at  the  expense  of  the 
former  at  temperatures  below  18°.  Evidently  the  great 
velocity  of  reaction  in  the  case  of  water  depends  upon 
the  presence  of  a  fluid  phase,  the  water.  Superheated 
ice  is  not  known,  whereas  the  two  allotropic  modifica- 
tions of  sulphur  or  of  tin  are  very  well  known  to  exist 
as  well  below  as  above  the  so-called  point  of  transition. 


14  THEORIES   OF   SOLUTIONS. 

These  processes  which  only  are  reverted  with  relative 
difficulty,  are  by  preference  regarded  as  chemical 
processes. 

Quite  recently,  after  the  evolution  of  the  theory  of 
electrolytic  dissociation  the  doctrine  of  the  utility  of 
solvents  for  the  progress  of  chemical  reactions  has 
been  put  in  a  new  light.  This  is  especially  true  for 
water,  but  also  for  alcohols  and  many  other  solvents, 
in  which  dissolved  substances  dissociate  into  their  ions. 
Gore  had  for  instance  observed  that  the  ability  of 
hydrochloric  acid  to  .dissolve  oxides  and  carbonates  of 
the  alkali-metals  or  alkaline  earth-metals  depends  upon 
the  presence  of  water.  This  was  stated  by  Hittorf, 
who  did  not  believe  that  Gore's  experiments  were 
conclusive,  and  even  he  found  the  same  peculiarity 
with  anhydrous  hydrobromic  and  hydriodic  acid.  The 
water-free  acids  are  non-conductors  of  electricity  and 
do  therefore  not  contain  ions  hi  appreciable  degree. 

Most  reactions  and  especially  the  most  important 
ones  in  inorganic  chemistry  are  due  to  ions — they  are 
characterized  by  their  instantaneous  accomplishment. 
This  idea  is  carried  out  by  Ostwald  in  his  treatise  on 
chemical  analysis. 

The  presence  of  moisture  is  of  the  greatest  importance 
for  many  reactions,  as  has  been  shown  by  Dixon  and 
Baker.  This  action  of  water  is  often  attributed  to  the 
formation  of  small,  generally  invisible  droplets,  in 
which  the  reacting  substances  dissolve.  This  view  has 
been  emphasised  by  D.  K.  Zavrieff. 

It  would  be  too  rash  to  conclude  from  these  observa- 
tions that  other  substances  than  (the  common)  ions 
do  not  react.  The  formation  of  nitro-compounds  of 


HISTORY  OF  THE  THEORY  OF  SOLUTIONS.  15 

derivatives  of  benzol,  for  instance,  is  not  due  to  the  ions 
H  or  N03  of  nitric  acid.  The  reaction  goes  on  the  more 
rapidly  and  the  reaction  is  the  more  complete,  the 
higher  the  concentration  is  of  the  nitric  acid.  For 
producing  the  tri-nitro-derivates  an  addition  of  oil  of 
vitriol  is  necessary,  which  binds  the  water  formed  during 
the  process  (for  instance  in  the  nitration  of  benzene): 

C6H6  +  HON02  =  H2O  +  C6H5  -  N02 

Probably  benzene  is  to  a  very  small  degree  dissociated 
electrolytically  into  the  ions  H  and  C6H5  and  the  nitric 
acid  in  high  concentration  into  N02  and  OH  of  which 
H  and  N02  are  positively  charged.  On  addition  of 
water  the  ions  HO  and  N02  decrease  and  are  transformed 
into  the  ions  H  and  N03.  Therefore  the  reaction 
diminishes.  Of  course  this  view  is  only  a  modern 
modification  of  the  old  conception  of  radicals.  Similar 
ideas  may  be  adapted  for  the  explanation  of  any  chem- 
ical reaction  from  the  electrolytic  standpoint. 

Sometimes  it  has  been  stated  that  water  is  not 
favorable  for  reactions.  Thus  H.  Goldschmidt  and  his 
pupils  found  that  the  formation  of  esters  of  organic  acids 
with  alcohol  is  hampered  by  traces  of  water.  Gold- 
schmidt expressed  the  opinion  that  the  hydrogen  ion  of 
the  acid  forms  a  complex  ion  C2H5OH.H  through  addi- 
tion of  alcohol.  This  ion,  he  supposes,  is  the  really 
reacting  one  and  is  spoiled  by  the  presence  of  water. 
(It  seems  to  me  more  simple  to  suppose  that  alcohol  is 
partially  dissociated  into  the  ions  C2H5  and  OH  and  that 
the  C2H5  ion  decreases  on  addition  of  H.OH  with  its 
relatively  great  quantity  of  OH-ions,  and  that  the  ion 
C2H5  replaces  the  H  ion  in  the  acid).  Similar  circum- 


16  THEORIES  OF   SOLUTIONS. 

stances  have  been  observed  in  a  great  number  of  re- 
actions in  organic  chemistry.  Here  is  a  vast  field  of 
interesting  investigations  for  the  extension  of  the 
theory  of  electrolytic  dissociation. 


LECTURE    II. 

THE  MODERN  MOLECULAR  THEORY. 

AT  the  end  of  the  eighteenth  century  a  great  develop- 
ment of  chemistry  took  place  and  from  this  time  we 
date  modern  chemistry.  It  is  usually  said  that  we  are 
indebted  to  Lavoisier  for  this  wonderful  progress.  I 
believe  it  is  better  to  say  that  the  great  change  was 
due  to  the  application  of  quantitative  methods  in 
chemistry.  Certainly  there  had  been  quantitative 
measurements  made  before  but  only  on  a  small  scale. 
It  was  at  that  time  that  Cavendish  made  his  excellent 
measurements,  amongst  which  the  determination  of  the 
composition  of  water  was  the  for  our  science  most 
significant.  Lavoisier  seems  to  have  known  of  this 
experiment,  but  he  made  it  anew  and  carried  out  some 
new  analogous  experiments  in  which  he  proved  that 
the  quantity  of  matter  is  not  changed  in  chemical 
reactions,  a  view  which  had  already  been  expressed 
by  van  Helmont  (1577-1644).  But  it  was  Lavoisier 
who  with  admirable  consistency  carried  through  this 
idea  and  so  inaugurated  a  new  era.  Yet  he  was  not 
alone,  the  time  was  ripe  for  the  revolution  of  chemical 
science.  Richter  studied  (1792-1794)  the  phenomenon 
of  neutralization  of  solutions  and  found  that  if  a 
certain  quantity  of  an  acid  solution  neutralizes  a  given 
quantity  of  alkali  and  the  same  is  true  for  a  definite 
quantity  of  another  acid  solution,  then  these  two  acid 
solutions  are  also  equivalent  in  the  neutralization  of  a 

3  17 


18  THEORIES  OF  SOLUTIONS. 

second  basic  substance.  Further  Scheele  had  found 
that  some  metals  can  attain  to  more  than  one  stage  of 
oxidation.  Richter  came  to  the  conclusion  that  these 
different  stages  neutralize  quantities  of  one  and  the 
same  acid,  which  are  proportional  to  then*  content  of 
oxygen.  In  his  controversy  with  Berthollet  Proust 
proved  that  there  may  be  different  stages  of  oxidation 
of  the  same  substance,  e.  g.,  iron  and  tin,  but  that  no 
intermediate  products  between  the  few  well-defined 
compounds  of  constant  proportions  are  to  be  found. 
It  is  very  remarkable,  that,  as  Le  Chatelier  says, 
Proust's  analyses,  from  which  he  deduced  his  conclu- 
sions "were  often  very  poor,  and  he  gave  analyses, 
which  did  not  at  all  correspond  with  the  facts." 

Quite  the  same  we  may  say  of  Dalton.  In  his  first 
publication  (1803)  he  gave  the  following  analyses,  in 
which  N  expresses  4  unit-weights  of  nitrogen,  0  5.66  of 
oxygen,  H  1  of  hydrogen,  C  4.5  of  carbon  and  S  17 
unit-weights  of  sulphur: 

Nitrous  oxide  . . .  N2O  Ammonia NH 

Nitrous  gas NO  Oxide  of  carbon ....  CO 

Nitrous  acid N20s  Carbonic  acid CO2 

Nitric  acid NO2  Sulphurous  acid SO 

Water HO  Sulphuric  acid S02 

Marsh  gas CH2  Olefiant  gas CH. 

According  to  these  figures  the  anhydride  of  sulphuric 
acid  ought  to  contain  double  the  quantity  of  oxygen 
for  the  same  weight  of  sulphur  as  sulphurous  acid 
whereas  we  now  know  that  this  ratio  is  as  3 : 2.  Water 
has  according  to  Dalton  the  composition  1  part  of 
hydrogen  to  5.66  oxygen,  the  right  proportion  is  1  to  8, 
and  so  forth. 

It  is  said  that  Dalton  was  the  founder  of  the  modern 


THE  MODERN  MOLECULAR  THEORY.        19 

atomic  theory  and  although  that  is  to  a  certain  extent 
true,  yet  on  the  other  hand  it  is  just  as  certain  that, 
if  Dalton  and  Proust  had  not  very  firmly  believed  the 
atomic  theory,  which  prevailed  at  that  time,  they 
would  not  have  been  led  to  its  foundation  through 
their  very  imperfect  analyses.  Yet  there  was  some- 
thing new  of  great  importance  in  their  atomic  theory, 
compared  with  that  of  the  old  Greek  philosophers. 
The  latter  had  only  said  that  matter  was  built  up  of 
atoms  of  different  size  and  form.  They  did  not  recog- 
nize what  we  call  elements,  their  elements  corresponded 
to  qualities.  Therefore  they  had  no  ground  to  suppose 
that  the  atoms  of  the  same  substance  have  always  the 
same  mass.  But  the  hypothesis  that  this  is  the  case 
is  most  obvious  as  Dalton  explains.  Water,  he  says, 
has  always  the  same  composition.  If  then  it  always 
contains  the  same  number  of  hydrogen  and  of  oxygen 
atoms,  as  he  believed,  the  only  reasonable  explanation 
is  to  suppose  that  all  atoms  of  hydrogen  are  absolutely 
similar  to  each  other,  and  that  a  given  atom  of  oxygen 
does  not  differ  at  all  from  any  other  atom  of  oxygen. 

Immediately  after  these  experiments  Wollaston 
showed  that  Dalton's  law  of  multiple  proportions  is 
also  valid  for  the  neutralization  of  acids  with  bases. 
So,  for  instance,  he  gave  an  analysis  indicating  that 
bicarbonate  of  sodium  contains  double  the  quantity 
of  carbonic  acid  to  the  same  weight  of  sodium,  as  the 
monocarbonate  does.  At  the  same  time  that  Dalton 
was  working  Berzelius  was  executing  with  marvellous 
diligence  a  great  number  of  excellent  analyses  of  the 
most  varied  substances,  and  all  chemists  followed  his 
example  and  carried  out  accurate  quantitative  measure- 
ments. 


20  THEORIES   OF   SOLUTIONS. 

In  1805  Gay-Lussac  discovered  the  fundamental 
law  that  the  volumes  of  two  gases,  which  combine  to 
form  a  compound,  stand  in  a  simple  numerical  relation, 
for  instance  the  volumes  of  hydrogen  and  oxygen 
entering  into  water  are  in  the  proportion  2  to  1,  those 
of  hydrogen  and  nitrogen  entering  into  ammonia  as 
3  to  1,  etc.  This  discovery  led  later  on  to  the  law  of 
Avogadro. 

From  the  beginning  of  the  last  century  the  system 
of  quantitative  measurements  had  put  its  stamp  on 
chemistry  and  from  that  time  dates  modern  chemical 
science  rather  than  from  the  tune  when  oxygen  was 
discovered.  The  great  progress  made  in  chemistry 
towards  the  end  of  the  last  century  when  modern 
physical  chemistry  was  inaugurated,  depended  also 
upon  the  introduction  on  a  large  scale  of  new  quanti- 
tative measurements. 

After  Dalton  had  established  the  law  of  multiple 
porportions  it  would  seem  that  the  atomic  theory  had 
won  an  absolutely  undisputable  victory  for  all  times. 
When  the  mechanical  theory  of  heat  had  begun  its 
triumphal  march  through  the  exact  sciences  it  allied 
itself  with  the  atomic  theory  as  an  equal,  the  kinetic 
theory  of  gases  was  born  and  developed  by  the  fore- 
most physicists,  such  as  Clausius,  Maxwell,  and  Boltz- 
mann.  They  calculated  the  motions  and  magnitude 
of  the  atoms  and  their  compounds,  the  molecules,  with 
nearly  the  same  certainty  as  an  astromoner  calculates 
the  magnitudes  and  the  motions  of  the  components  of 
double  stars.  The  atomic  theory  was  regarded  as  the 
firm  foundation  of  the  exact  sciences. 

Then  at  the  end  of  the  last  century  came  the  reac- 


THE  MODERN  MOLECULAR  THEORY.        21 

tion.  A  Bohemian  chemist,  Wald,  argued  in  the 
following  manner.  It  is  true  that  chemical  com- 
pounds have  a  constant  composition,  but  only  because 
we  demand  that  they  shall  have  it.  The  manufacturer 
subjects  them  to  different  physical  and  chemical  proc- 
esses such  as  recrystallization,  repeated  distillation, 
conversion  into  new  compounds  and  back  again  until 
the  composition  is  not  changed  by  them  but  the  same 
product,  that  is,  a  product  with  constant  physical 
and  chemical  properties  is  obtained  again  and  again. 
These  different  properties  are  of  course  dependent 
upon  the  composition  of  the  product,  in  other  words 
the  manufacturer  of  chemical  products  takes  good  care 
that  these  products  shall  have  a  constant  composition. 
And  according  to  Wald,  Nature  proceeds  in  the  same 
manner.  But  this  does  not  help  to  explain  why  we 
always  find  the  same  ratio  between  the  weight  of,  e.  g., 
oxygen  and  hydrogen  in  all  the  innumerable  organic 
compounds  which  we  now  know,  or  else  a  simple 
multiple  of  this  ratio.  To  explain  this  fact  a  new  law 
must  be  introduced,  which  expresses  just  this  assertion 
or  is  equivalent  to  it.  Ostwald  has  given  this  law  the 
name  of  "  the  law  of  integral  reactions. " 

There  is  still  a  difficulty  with  this  new  conception. 
There  exist  in  nature  substances  of  the  same  compo- 
sition but  of  different  properties.  The  simplest  case 
is  that  of  oxygen  and  ozone.  The  law  of  Avogadro 
leads  to  the  conclusion  that  if  a  molecule  of  oxygen 
contains  two  atoms  then  a  molecule  of  ozone  contains 
three  atoms.  The  atomic  theory  gives  a  new  mode  of 
variation  of  properties,  than  that  due  to  alteration 
of  composition,  namely  that  depending  on  change  of 


22  THEORIES  OF  SOLUTIONS. 

configuration  in  space.  Nature  also  gives  instances 
of  this  higher  degree  of  variability.  The  opponents 
of  the  atomic  theory  ought  therefore  to  invent  some 
other  explanation  than  that  of  Wald,  otherwise  then: 
case  remains  rather  weak. 

Nevertheless  Wald's  ideas  found  a  number  of  ad- 
herents, some  of  them  possessing  the  highest  authority 
such  as  Le  Chatelier  and  Ostwald,  and  the  latter  has 
worked  out  a  whole-  system  of  chemistry  on  the  founda- 
tion laid  by  Wald.  By  far  the  greater  majority  of 
chemists  had  not  listened  to  the  new  doctrines,  when 
a  wholly  new  aspect  of  the  question  came  up.  Eighty- 
four  years  ago  (1827)  an  English  botanist,  Robert  Brown, 
found  with  the  aid  of  the  microscope  that  small  particles, 
e.  g.,  grains  of  pollen,  suspended  in  a  fluid,  possess  a 
zig-zag  movement,  which  was  the  more  considerable 
the  smaller  the  particles  considered  were.  This  peculiar 
kind  of  motion  was  examined  by  a  great  number  of 
scientists,  from  Regnauld  1857  to  Gouy  1888,  and  they 
stated  one  after  the  other,  that  the  motion  in  question 
increases  with  the  smallness  of  the  particles,  the  fluidity 
of  the  surrounding  fluid  and  the  temperature.  It  was, 
to  put  it  briefly,  analogous  to  the  motion,  which  the 
adherents  of  the  kinetic  theory  of  gases  attributed  to 
the  molecules  of  a  gas.  Consequently  it  was  called 
the  Brownian  molecular  movement.  In  recent  times 
this  interesting  phenomenon  has  attracted  very  great 
attention.  Einstein  and  v.  Smoluchowski  have  de- 
veloped the  theory  of  it.  Svedberg,  Ehrenhaft  and 
especially  Perrin  have  investigated  it  experimentally. 
The  simplest  case  is  found  in  suspensions  in  air,  studied 
by  Ehrenhaft.  He  evaporated  silver  in  an  electric  arc. 


THE  MODERN  MOLECULAR  THEORY.        23 

The  vapours  condensed  to  extremely  small  drops. 
According  to  Stokes'  law  these  droplets  would  fall  the 
more  rapidly,  the  greater  their  magnitude.  By  these 
means  Ehrenhaft  could  separate  them  from  each  other 
according  to  their  size  and  when  he  knew  the  tune  re- 
quired for  their  subsidence  he  could  calculate  their 
dimensions.  Their  diameter  was  in  one  experiment 
only  about  the  thirty  thousandth  part  of  a  millimeter, 
so  that  they  could  only  with  difficulty  be  observed  with 
the  aid  of  an  ultramicroscope.  He  measured  their 
movement  and  found  it  to  be  0.046  millimeter  per 
second,  whereas  a  formula  of  v.  Smoluchowski  de- 
manded 0.048  millimeter  per  second,  a  really  good  agree- 
ment. 

Perrin  has  worked  out  his  experiments  on  a  very 
large  scale.  He  used  suspensions  of  gamboge  or 
mastich  in  water.  He  determined  the  distance,  d, 
between  the  position  of  a  droplet  at  the  beginning  and 
at  the  end  of  a  certain  time  (t).  The  droplet  describes 
a  straight  line  which  is  suddenly  altered  to  a  new  direc- 
tion every  time  that  the  droplet  in  its  movement  collides 
with  a  molecule.  Einstein  has  deduced  the  following 
formula: 

,2        R.T     1 

=  '' 


where  R  is  the  gas-constant  of  Avogadro's  law,  T  the 
absolute  temperature,  a  the  diameter  of  the  droplet, 
6  the  viscosity  of  the  surrounding  fluid  and  N  the  num- 
ber of  molecules  in  one  gram-molecule,  a  was  deter- 
mined by  means  of  Stokes'  law  from  the  velocity  with 
which  the  droplets  fell  in  water,  b  is  known,  as  well  as 


24  THEORIES   OF   SOLUTIONS. 

R  and  TT.  T,  t  arid  the  corresponding  values  of  d  were 
determined  experimentally.  He  found  N  =  68. 1022. 

Perrin  determined  the  value  of  N  in  another  way. 
The  kinetic  theory  demands  that  the  rotatory  energy 
of  a  droplet  should  be  of  the  same  magnitude  as  its 
translatory  energy.  From  this  theorem  Einstein  de- 
duced a  formula  connecting  .AT  with  the  velocity  of 
rotation  of  a  droplet.  The  droplets  convenient  for 
measurements  of  this  kind  must  be  relatively  large; 
Perrin  used  one  of  0.0115  millimeter  diameter.  Thanks 
to  foreign  matter,  often  appearing  in  such  droplets,  it 
is  possible  to  determine  their  velocity  of  rotation.  The 
droplets  were  maintained  floating  in  a  solution  of  urea 
of  their  own  density.  Perrin  found  the  number  N  = 
65.1022. 

Perrin  invented  yet  a  third  method  of  determining  N. 
It  is  well  known  that  the  density  of  our  atmosphere 
decreases  with  increasing  height.  This  depends  upon 
the  weight  of  the  upper  air-layers,  which  compress  the 
lower  ones.  The  rate  of  decrease  of  the  density  up- 
wards is  proportional  to  the  weight  of  one  molecule 
(according  to  the  gas- theory).  Now  Perrin  inquired 
whether  the  same  phenomenon  occurred  in  his  emul- 
sions— in  this  case  the  molecules  are  the  droplets  and 
then:  weight  is  diminished  by  the  weight  of  an  equal 
volume  of  water.  He  found  his  expectations  fulfilled 
and  could  by  the  aid  of  the  microscope  count  the 
number  of  droplets  in  different  heights  from  the  bottom 
of  the  vessel  containing  the  suspension.  From  these 
observations  he  could  calculate  how  many  times  one 
of  the  droplets  was  heavier  than  a  molecule  of,  for 
instance,  oxygen.  Further,  he  could  from  the  known 


THE  MODERN  MOLECULAR  THEORY.        25 

diameter  of  the  droplets  and  the  difference  of  their 
specific  weight  and  that  of  the  surrounding  fluid  calcu- 
late the  weight  of  each  droplet  in  the  fluid.  Hence  he 
could  calculate  the  absolute  weight  of  a  molecule  of 
oxygen  and  as  a  grammolecule  of  oxygen  is  32  grammes 
the  number  N  of  the  molecules  is  32  grammes  of  oxygen. 
He  found  a  value  of  N  =  71. 1022. 

All  the  three  values  determined  agree  exceedingly  well 
with  each  other  and  not  less  satisfactorily  with  the 
number  of  N,  found  by  other  methods.  These  are 
taken  from  different  parts  of  physical  science.  Fara- 
day's law  demands  that  the  total  charge  of  the  ions 
contained  in  1  gram  of  hydrogen  or  an  equivalent 
quantity  of  any  other  substance,  which  occurs  in 
the  form  of  electrolytic  ions,  should  be  96,550  coulombs. 
Now  Rutherford,  Geiger  and  Regener  have  counted 
the  number  of  a-particles  which  leave  a  given  quantity 
of  radium  per  second  and  they  have  also  measured 
the  quantity  of  electricity  on  a  single  a-particle,  which 
is  an  atom  of  helium  with  a  positive  charge.  Supposing 
now  that  an  atom  of  helium  is  charged  according  to 
Faraday's  law  and  equivalent  to  two  atoms  of  hydrogen, 
Rutherford  calculated  N  =  62. 1022.  Dewar  directly 
measured  the  quantity  of  helium  developed  during  a 
certain  time  from  one  gram  of  radium  and  found  from 
Rutherford's  figures  of  the  number  of  helium-atoms 
thrown  out  by  a  gram  of  radium  per  second,  that  N  = 
71. 1022.  Boltwood  calculated  the  quantity  of  «-par- 
ticles  emitted  by  one  gram  of  radium  and  the  corre- 
sponding number  of  radium-atoms  decomposed  in  a 
certain  time  and  compared  this  quantity  with  the 
observed  rate  of  decomposition  of  radium.  From  this 
calculation  the  result  is  obtained  that  N  =  71. 1022. 


26  THEORIES  OF   SOLUTIONS. 

Another  method  of  calculating  N  from  the  constants 
of  heat-radiation  gave  according  to  a  theory  of  Lorentz 
N  =  71.1022,  according  to  a  theory  of  Planck  N  = 
62.1022.  Townsend  determined  the  charge  of  droplets 
condensed  from  steam  by  means  of  Rontgen  rays.  He 
and  his  successors  found,  if  they  applied  the  law  of 
Faraday,  N  =  62. 1022  (on  the  average). 

There  are  several  other  methods  of  less  accuracy  but 
which  give  the  same  order  of  magnitude.  Thus  Cauchy 
determined  (1835)  the  number  of  molecules,  which 
when  laid  behind  one  another  at  molecular  distance 
on  a  straight  line  would  give  the  wave  length  of  the 
yellow  light  of  sodium  to  be  about  600.  Similar  deter- 
minations in  modern  tunes  are  due  to  Erfle,  and  al- 
though the  different  gases  do  not  give  the  same  values 
as  one  might  expect  (the  variation  is  about  as  3  to  4), 
they  agree  well  on  the  average  with  the  figures  of  Perrin. 
Lord  Rayleigh  determined  the  number  N  of  molecules 
hi  a  grammolecule  from  the  diffusion  of  light  from  the 
sky  and  found  N  about  70. 1022.  Also  from  the  internal 
friction  of  gases  when  compared  with  the  volume  in 
the  condensed  state  or  the  refractive  index,  the  dimen- 
sions and  number  of  the  molecules  has  been  deduced, 
giving  N  about  45. 1022. 

When  we  know  the  number  N  it  is  easy  to  calculate 
the  diameter  of  the  molecules.  It  varies  between 
about  2.10-8  and  6.10-8  cm. 

We  see  then  that  the  molecular  or  atomic  theory  has 
attained  a  very  high  degree  of  probability  through  these 
recently  made  measurements.  Ostwald  has  openly  con- 
ceded that  this  theory  does  not  seem  open  to  question 
but  that  one  must  admit  a  granular  structure  of  matter. 


THE  MODERN  MOLECULAR  THEORY.        27 

But  not  only  matter  is  regarded  as  having  an  atomic 
structure.  In  1870  Helmholtz  indicated  that  the  most 
simple  way  of  interpreting  the  law  of  Faraday  is  to 
suppose  that  there  exist  ultimate  small  quantities  of 
electricity,  which  are  all  of  the  same  magnitude  and 
that  one  of  these  electrical  particles,  now  called  elec- 
trons, is  what  is  united  with  a  monovalent  ion.  It  has 
not  yet  been  found  possible  to  isolate  a  positive  electron, 
but  the  negative  electrons  occur  in  the  so-called  cathode- 
rays  or  j8-rays.  It  is  therefore  now  generally  admitted 
that  the  charge  of  positive  ions  is  due  to  the  loss  of 
negative  electrons.  The  ultimately  small  quantity  of 
electricity  is  about  46.10~10  electrostatic  units  and  it 
was,  as  a  matter  of  fact,  the  determination  of  this 
electrical  quantity  which  led  to  the  calculation  of  the 
number  N  by  means  of  electrical  methods  and  which 
yielded  concordant  results  before  the  direct  measure- 
ment of  N  by  Perrin  and  Ehrenhaft  on  suspended 
particles. 

Science  changes  its  aspect  very  rapidly  nowadays. 
When  Ehrenhaft  measured  the  movements  of  elec- 
trically charged  particles  under  the  influence  of  gravita- 
tion and  electric  forces,  he  observed  that  the  electric 
forces  and  hence  the  electric  charges  found  for  different 
single  particles  were  not  of  the  same  magnitude  but 
differed  from  one  another  in  a  rather  high  degree. 
The  old  determinations  of  the  atomic  charge  were  all 
founded  on  a  mean  of  the  movements  of  the  charged 
particles.  Now  Ehrenhaft  studied  the  behaviour  of  a 
single  particle.  He  prepared  these  particles  by  evap- 
orating the  noble  metals  gold,  silver  or  platinum  in  the 
electric  arc.  These  particles  were  as  a  rule  very  heavy 


28  THEORIES   OF   SOLUTIONS. 

so  that  the  Brownian  movement  did  not  render  the 
observations  difficult.  In  moist  air  or  if  temperature- 
currents  were  not  excluded  the  Brownian  movement 
was  very  perceptible.  The  same  was  the  case  with 
the  droplets  formed  in  the  neighbourhood  of  a  piece  of 
yellow  phosphorus. 

The  charge  of  the  metallic  particles  observed  by 
Ehrenhaft  varied  for  platinum  between  0.9  and  12. 10-10 
units  (instead  of  the  constant  charge  4.65. 10~10  units), 
for  silver  between  0.9  and  26.7. 10-10  units  and  for  gold 
between  0.5  and  9.6. 10~10  units.  It  seemed  therefore 
that  charges  about  ten  times  less  than  the  charge  of 
an  ion  may  sometimes  occur.  Amongst  the  observed 
charges  some  are  found  to  possess  a  preponderating 
frequency  and  these  commonly  occurring  charges  do 
not  differ  very  much  from  the  mean  electric  charge 
observed  by  himself  and  his  predecessors.  Simul- 
taneously with  Ehrenhaft  (1910)  Millikan  arrived  at 
similar  results. 

The  observations  of  Ehrenhaft  were  continued  by  K. 
Przibram.  He  investigated  the  charge  of  droplets 
formed  during  electrolytic  production  of  oxygen  or 
upon  the  admixture  of  air,  through  which  electric 
sparks  had  passed,  with  moist  air,  or  in  the  evaporation 
of  hydrochloric  acid  in  air  ionized  by  means  of  Rontgen- 
rays  or  finally  formed  in  the  neighbourhood  of  yellow 
phosphorus  in  air.  He  arrived  at  results  which  agree 
very  well  with  those  of  Ehrenhaft. 

In  Przibram's  measurements  the  individual  charges 
varied  for  electrolytic  oxygen  between  1.4.10-10  and 
170. 10-10  electrostatic  units,  for  particles  produced  by 
electric  discharges  in  moist  air  the  corresponding  figures 


THE  MODERN  MOLECULAR  THEORY.        29 

were  1.7  and  191,  for  drops  in  nebulae  from  hydrochloric 
acid  2.2  and  60,  and  finally  for  drops  from  nebulae  in 
moist  air  in  the  presence  of  phosphorus  in  one  series  of 
about  180  measurements  0.7  and  120  in  another  series 
with  about  1000  single  measurements  where  we  might 
have  expected  a  greater  variation,  2.7  and  52  respec- 
tively. It  is  very  difficult  to  see  a  simple  way  out  of 
the  difficulties  raised  by  Ehrenhaft  and  Przibram.  A 
charge  of  10-10  electrostatic  units  per  particle  corre- 
sponds to  1.29.1020  molecules  in  one  cc.  of  gas  at  0°  and 
760  mm.  pressure  or  28,900. 1020  molecules  in  one 
grammolecule.  If  the  charge  of  a  single  particle  is 
n.10-10  electrostatic  units  the  number  of  molecules  is 
n  times  less. 

In  his  observations  the  frequency  of  different  charges 
shows  a  periodicity  with  maxima  in  nearly  equal  dis- 
tances. Thus  the  mean  distance  of  the  thirteen  maxi- 
ma in  a  series  of  observations  with  droplets  from 
phosphorus  is  4.7.10-10  electrostatic  units,  very  near 
to  the  atomic  charge  according  to  older  measurements. 
Yet  even  this  regularity  seems  to  be  to  a  certain  degree 
fortuitous.  In  series  carried  out  on  different  days  with 
droplets  from  phosphorus  Przibram  found  this  interval 
varying  between  3.10-11  and  7.10-10  electrostatic  units. 
The  general  mean  was  still  4.6. 10-10  units.  The  cause 
of  this  peculiar  variation  is  still  undetected.  In  order 
to  get  a  reliable  average  value  it  seems  necessary  to 
make  thousands  of  single  observations. 

In  some  hundred  cases  Przibram  succeeded  in  meas- 
uring the  charge  of  the  same  droplet  twice  during  its 
fall,  and  he  found  that  in  many  cases  a  discharge  had 
taken  place. 


30 


THEORIES  OF  SOLUTIONS. 


It  should  be  mentioned  here  that  de  Broglie  has 
carried  out  similar  measurements  to  those  of  Ehrenhaf t 
without  finding  corresponding  anomalies.  A  concise 
summary  of  the  present  state  of  the  question  of  the 
atomistic  structure  of  electricity  is  given  hi  the  table 
below,  reproduced  from  Ehrenhaft's  last  memoir. 

Table  of  the  chief  determinations  of  the  unit  charge, 
according  to  F.  Ehrenhaft. 

e.  10" 
R.  v.  Helmholtz  and  f  Quantity  of  electricity 

THrharr  1SQO  1  2Q  at     6  le  C  t  TO  ly  8 18. 

Richarz ....      . .  1890        1.29  J       L^d^^g  number 

E  J^tonev  1890        1 29-6 1  of  atoms  'm  a  cubic 

E.  J.  btoney 1890        1.29-6.1  ^     centimeter  gas. 

"  Falling  nebula  of  drops. 

T.  S.  Townsend 1898  1.2-1.5  .,  Stokes  formula.  De- 
ll. T.  Lattey (1909)  5  termination  of  the 

total  charge. 

f  Falling  nebula  of  drops. 

J.  J.  ThomBon 1898-99  6.5-6.8(6.0-8.4)^      ££3±£ulSf  ?be 

I     total  charge. 

f  Constants  of  radiation 

M-Di  „  i,  1ftni         ,.  Aft  J      entering  in  the  for- 

•  Planck 1901        4'69  mulae  of  Stefan  and 

L     W.  Wien   (Planck). 

I.  Nabl 1902        2  Charges  of  gases  with 

drops  from  Wehnelt- 
interruptor. 

J.  J.  Thomson 1903        3.4  (3.3-3.5)          lonization    through 

radium. 

H.  A.  Wilson 1903        3.1  (2.0-4.4)          Falling  of  water  drops 

in  electric  fields. 

H.  Pellat 1907        2.46-6.9  Mobility  of  ions  in  elec- 

trolytic solutions. 

K.  Przibram 1907        3.8  (1.7-6.2)          Falling  of  alcohol  drops 

in  electric  fields. 
R.  H.  Millikan  and 

L.  Begeman 1908        4.03  (3.66-4.37)     Method  of  H.  A.  Wil- 
son. 
E.  Rutherford  and 

H.  Geiger 1908        4.65  (4.15-5.5)       Counting  of  o-particles, 

measuring  of  charge. 


THE  MODERN  MOLECULAR  THEORY. 


31 


E.  Regener 1908        4.79 


R.  Tabor  and 
R.  T.  Lattey. 

A.  Alexejew  and 
M.  Malikow  . 
F.  Ehrenhaf t . . 


1909        4.47  (3.13-5.74) 


G.  Moreau  .... 
M.  deBroglie. . 
J.  Perrin  . 


.1909 
1909 

.1909 
.1909 
,1909 


R.  A.  Mfflikan  .,    ..1910 


F.  Ehrenhaft..       ..1910 


K.  Przibram..       ..1910 


4.5  (3.0-6.3) 
4.46-4.68 

4.3  (4.1-4.8) 

4.5 

4.11 

4.05 
4.50 
4.66 


0.9-12.4  (Pt) 
0.9-26.7  (Ag) 
0.5-9.6  (Au) 
0.5-28.9  (P) 
3.45  (O) 
4.2  (air) 
4.15  (HC1) 
4.7  (P). 


Counting  of  o-particles, 
measuring  of  charge. 

Electrolytic  nebula  of 
oxygen. 

H.  A.  Wilson's  method 

Single  particles  falling 
in  air. 

Mobility  of  ions  from 
flames. 

Smoke  of  cigarettes. 
Formula  of  Einstein. 

From  the  distribution 
of  particles.  N  =  70.5 
.  1022 

From    the     Brownian 
movement 
N -71.5.  10" 

From  the  rotation  of 
particles 
N=65.  1022 

Single  drops  in  electric 
field    2e  =  8.60-10.07, 
3e  =  13.45-13.99. 
4e  =  17.46-19. 10. 
5e=22.52-24.14. 
6e= 26.89-29.82. 

Occurrence  of  maxima 
of  frequency  in  the 
distribution  of  in- 
dividual charges. 

Distances  of  maxima  of 
frequency  in  the  dis- 
tribution of  individ- 
ual charges. 


It  seems  very  difficult  to  explain  the  deviations  ob- 
served by  Ehrenhaft  and  Przibram  from  the  atomistic 
theory  of  electricity.*  The  accuracy  of  the  law  of  Stokes 

*After  this  had  been  written,  some  very  important  memoirs  of  Milli- 
kan  and  of  Perrin  and  his  collaborators,  Roux  and  Bjerrum,  have  ap- 


32  THEORIES   OF   SOLUTIONS. 

has  been  very  thoroughly  investigated  and  confirmed 
in  similar  cases,  so  that  a  deviation  from  it  of  the 
necessary  magnitude  seems  unlikely.  Further,  through 
such  an  expectation  all  the  former  measurements 
indicating  the  atomic  division  of  electricity  would  be- 
come invalidated.  It  has  however  been  observed  in 
many  cases  that  exceptions  from  Stokes'  law  occur  with 
particles  which  are  not  spherical,  for  instance,  with  the 
crystalline  particles  of  sal  ammonia.  Other  deviations 
from  this  law  occur  with  very  minute  spheres.  As 
matters  stand  at  present  the  proof  of  the  granular  or 
atomic  distribution  of  matter  rests  chiefly  on  the  ob- 
servations of  the  movement  of  small  suspended  particles 
in  a  surrounding  liquid.  A  system  of  this  nature  is 
called  a  colloidal  solution;  in  the  experiments  cited  above 
the  particles  were  very  coarse. 

It  is  a  matter  of  great  interest,  that  the  celebrated 
mathematical  physicist  Planck  has  tried  to  introduce 
an  atomistic  view  of  the  radiant  energy.  Thus  a  body 
emitting  radiant  heat  should  not  lose  its  energy  con- 
tinuously but  in  discrete  portions,  which  are  constant 
for  radiated  energy  of  the  same  wave-length,  but  are  in 
general  inversely  proportional  to  this  quantity.  Stark 
has  endeavored  to  confirm  this  theorem  of  Planck  by 
showing  that  canal  rays  do  not  emit  a  particular  type 
of  radiation  until  they  have  reached  a  certain  velocity, 
i.  e.,  possess  a  sufficient  quantity  of  energy.  Other 
experiments  of  Ladenburg  regarding  corpuscles  emitted 
by  bodies  exposed  to  ultraviolet  light  seem  also  favor- 
able to  Planck's  hypothesis.  This  theorem  of  the 

peared.  They  have  subjected  Ehrenhaft's  and  Przibram's  experiments 
to  a  severe  criticism,  and  they  find  a  quite  constant  value  of  e.  Milli- 
kan  gives  e  =4.9  .  10~10  and  Perrm  e  =4.2  .  10"10. 


THE  MODERN  MOLECULAR  THEORY.        33 

discrete  structure  of  energy  depends  entirely  upon  that 
of  the  atomic  distribution  of  electric  charges,  and  it 
will  therefore  be  our  first  problem  to  clear  up  the 
question  raised  by  Ehrenhaft,  before  we  try  to  give 
an  answer  to  the  much  more  difficult  problem  raised 
by  Planck,  whose  theory  has  been  recently  attacked  by 
Sir  J.  J.  Thomson,  who  gave  a  wholly  different  expla- 
nation of  the  phenomenon  observed  by  Ladenburg. 

In  a  very  interesting  manner  Svedberg  has  also 
shown  that  molecules  of  a  real  solution,  namely  of 
polonium  chloride,  are  in  constant  motion  and  exactly 
of  the  order  of  magnitude  demanded  by  theory.  The 
number  of  a-particles  emitted  by  a  solid  radioactive  sub- 
stance in  unit  time  is  not  constant  but  changes  accord- 
ing to  the  theory  of  probability.  If  n  is  the  mean  value 
of  this  number,  the  relative  mean  deviation  d  from  this 
number  is  proportional  to  1/i/w  according  to  a  theory 
given  by  v.  Schweidler.  This  theorem  was  verified  by 
Regener. 

If  we  investigate  a  dissolved  radioactive  substance 
and  with  the  microscope  observe  the  a-particles  emitted 
in  unit  tune  from  a  given  volume  of  the  solution  by 
means  of  the  scintillations  produced  on  a  screen  of  zinc 
sulphide,  then  the  variation  of  n  must  be  greater  than 
in  a  solid  preparation,  because  the  molecules  are  moving 
out  of  and  into  the  observed  volume.  If  the  relative 
mean  deviation  from  the  mean  number  of  radioactive 
molecules  due  to  this  mobility  is  di  —  di  may  be  calcu- 
lated from  a  theoretical  formula  of  v.  Smoluchowski 
—  then  the  total  relative  variation  D  due  to  the  two 
circumstances  is  according  to  the  theory  of  probabilities 


D  =  i/d2  + 

4 


34  THEORIES  OF  SOLUTIONS. 

Svedberg  once  observed  a  solid  preparation  of  a 
polonium  deposit  on  copper,  another  time  a  solution  of 
polonium  chloride.  He  found  for  the  solid  preparation 
d=42.3  per  cent,  instead  of  the  calculated  number  42.8 
per  cent.,  when  n  was  0.559  per  second.  For  the  solu- 
tion he  found  when 

n=  0.476  0.349  0.224 

Dob. =55.3  71.5  83.4 

D«oc=58.6  68.8  80.5 

dcaic=46.4  54.1  67.6 

The  agreement  between  the  observed  and  calculated 
values  of  D  is  very  good,  and  the  difference  from  the 
calculated  values  for  immobile  molecules  (d  calc.)  is 
rather  great,  so  that  the  movement  of  the  dissolved 
molecules  seems  to  be  well  proved. 

Through  these  many  measurements  of  different  kinds 
and  especially  through  the  study  of  the  Brownian 
movement,  the  law  of  Avogadro,  that  a  given  number 
of  molecules  of  any  gas  at  a  fixed  temperature  and 
pressure  (e.  g.,  0°  C.  and  1  atmosphere)  fill  the  same 
volume  (under  the  conditions  mentioned,  22,410  cm.  for 
2  grams  of  hydrogen  or  one  grammolecule  of  any  gas), 
is  supported  and  the  difference  between  atom  and 
molecule  which  had  been  foreseen  by  Gassendi  and 
established  by  Avogadro,  is  thereby  proved  to  be  real. 
And  furthermore  the  kinetic  theory  of  matter  has  been 
demonstrated.  The  use  of  equivalent  weights  instead 
of  atomic  weights  which  prevailed  in  French  literature 
on  chemistry  a  few  years  ago  and  which  was  actuated 
by  a  doubt  regarding  the  real  existence  of  molecules, 
has  no  longer  any  adherents. 

It  is  very  curious  that  Dalton  in  his  "New  System  of 
Chemical  Philosophy"  (1808)  repudiated  the  law  of 


THE  MODERN  MOLECULAR  THEORY.        35 

Avogadro,  published  three  years  later.  Dalton  says, 
"At  the  time  I  formed  the  theory  of  mixed  gases,  I 
had  a  confused  idea,  as  many  have,  I  suppose,  at  this 
time,  that  the  particles  of  elastic  fluids  are  all  of  the 
same  size;  that  a  given  volume  of  oxygenous  gas  con- 
tains just  as  many  particles  as  the  same  volume  of 
hydrogenous  .  .  .  But  ...  I  became  convinced, 
that  different  gases  have  not  their  particles  of  the  same 
size."  In  another  place  he  says,  "No  two  elastic 
fluids,  probably,  have  the  same  number  of  particles, 
either  in  the  same  volume  or  the  same  weight."  To 
Gay-Lussac's  law  of  the  simple  proportions  of  the  vol- 
umes of  combining  gases  he  objects:  "In  no  case,  per- 
haps, is  there  a  nearer  approach  to  mathematical 
exactness,  than  in  that  of  one  measure  (volume)  of 
oxygen  to  two  of  hydrogen  (when  they  combine  to  form 
water);  but  here  the  most  exact  experiments  I  have 
ever  made  gave  1.97  hydrogen  to  1  oxygen." 

It  is  a  great  pity  that  Dalton  objected  so  strongly 
to  the  validity  of  what  we  now  call  Avogadro 's  law, 
for  otherwise  he  would  have  given  a  much  more  perfect 
atomic  theory  and  probably  the  progress  of  science 
would  have  gone  on  more  rapidly  than  it  did  a  century 
ago. 


LECTURE  III. 

SUSPENSIONS. 

THROUGH  the  work  of  Perrin  it  has  been  proved  that 
small  particles  which  without  difficulty  may  be  ob- 
served through  an  ordinary  microscope  behave  as 
molecules  hi  a  gas.  Further  Svedberg  made  out 
experimentally  that  the  molecules  in  a  liquid,  namely 
a  solution  of  polonium  chloride,  which  are  much  more 
nearly  related  to  those  of  a  gas  behave  in  quite  the  same 
manner. 

Fluids  containing  suspended  particles  have  attrac- 
ted a  very  great  interest  in  recent  tunes;  therefore  a 
short  review  of  their  properties  will  be  very  appro- 
priate in  this  place. 

There  are  many  methods  of  preparing  such  suspen- 
sions. The  simplest  one  consists  in  dissolving  in 
alcohol  a  substance,  e.  g.,  mastich,  which  is  insoluble 
in  water,  and  pouring  a  quantity  of  this  solution  into 
water.  Then  the  alcohol  is  taken  up  by  the  water 
and  the  particles  of  mastich  remain  as  a  mist  floating 
in  the  water.  Another  very  simple  method  is  to 
grind  some  substance  to  a  fine  powder  and  throw  it 
into  a  fluid  which  does  not  dissolve  it,  e.  g.,  kaoline 
with  water.  Other  methods  are  founded  on  chemical 
properties.  If  sulphuretted  hydrogen  (H2S)  is  intro- 
duced into  an  aqueous  solution  of  arsenious  acid  (As2O3) 
a  formation  of  arsenious  sulphide  (As2S3)  occurs  and 
this  remains  suspended  in  the  fluid.  The  superfluous 

33 


SUSPENSIONS.  37 

H2S  may  be  removed  from  the  fluid  by  bubbling  an 
indifferent  gas  through  it.  In  a  similar  manner  a  sus- 
pension of  sulphide  of  antimony  (Sb2S3)  may  be  pre- 
pared. In  other  cases  sulphuretted  hydrogen  is 
introduced  into  a  dilute  solution  of  a  metallic  salt 
(for  instance  salts  of  iron,  cobalt,  nickel,  palladium  or 
platinum),  and  a  sulphide  is  formed,  which  remains 
partially  suspended  in  the  liquid.  At  the  same  time 
the  acid  of  the  salt  is  set  free;  to  remove  it  the  solution 
is  placed  in  a  dialyser,  which  allows  the  acid  to  pass 
through  but  not  the  suspended  grains.  In  an  analogous 
manner  it  is  possible  to  prepare  suspensions  of  nearly 
all  insoluble  salts.  Some  salts,  e.  g.,  ferric  acetate 
(Graham)  or  thorium  nitrate  are  hydrolysed  into 
hydrate  and  acid  by  the  solvent  water  and  then  the 
hydrate  often  remains  in  suspension  if  the  acid  is 
dialysed  away.  This  fact  that  suspended  particles 
may  be  separated  from  salts  by  means  of  dialysis 
is  the  reason  why  the  name  of  colloids  has  been  given 
to  them.  Graham  had  as  a  matter  of  fact  (1862) 
called  substances  such  as  glue,  egg-albumen,  gum- 
arabic,  etc.,  which  do  not  pass  through  parchment- 
paper  colloids  (from  kolla,  glue)  in  contradistinction  to 
crystalloids,  which  pass  easily  through  the  membrane. 
But  the  suspensions  have  very  little  similarity  to  glue 
or  albumen  and  therefore  the  name  of  colloid  should 
be  rejected  in  this  special  case. 

Another  method  of  preparing  suspensions  of  noble 
metals  was  introduced  by  Bredig.  He  dipped  two 
rods  of  the  metal  into  water  and  connected  the  free 
ends  of  the  rods  with  a  powerful  electrical  machine. 
Then  an  electric  arc  was  formed  between  the  rods, 


38  THEORIES  OF  SOLUTIONS. 

when  these  were  brought  near  to  each  other.  The 
metals  evaporated  and  condensed  to  a  fine  dust  which 
remained  to  some  extent  suspended.  It  gave  a  char- 
acteristic colour  to  the  liquid,  greenish  brown  for  silver, 
dark  brown  for  platinum  and  red  or  blue  for  gold  (the 
blue  colour  corresponds  to  coarse  particles).  This 
method  cannot  be  used  for  common  metals  as  they 
react  with  the  water.  But  hi  other  liquids  such  as 
alcohols,  ether,  esters  Svedberg  succeeded  in  preparing 
suspended  ordinary  metals  by  using  alternating  cur- 
rents. 

The  physical  properties  of  such  suspensions  may  be 
regarded  as  an  arithmetic  mean  between  those  of  the 
surrounding  fluid  and  of  the  suspended  matter.  As 
the  latter  is  generally  present  only  to  a  very  small 
extent,  the  general  physical  properties  are  very  similar 
to  those  of  the  liquid.  As  the  colour  of  the  suspended 
particles,  especially  for  metals,  is  strongly  marked  the 
suspension  has  generally  a  characteristic  colour.  Sved- 
berg found  that  this  colour  for  alkali-metals  suspended 
in  ether  is  very  similar  to  that  of  their  gases.  The 
suspensions  are  opaque  and  show  the  so-called  phe- 
nomenon of  Tyndall,  i.  e.,  if  a  strong  beam  of  light  falls 
upon  them,  it  illuminates  the  suspended  particles  and 
its  path  may  be  seen  from  the  side.  This  reflected  light 
is  polarized.  It  gives  consequently  a  means  of  detect- 
ing the  particles,  even  if  they  are  so  small  that  they 
cannot  be  seen  with  the  aid  of  a  microscope  (droplets 
of  a  diameter  less  than  about  0.0002  mm.).  This  is 
effected  by  the  ultramicroscope,  which  was  independ- 
ently invented  by  Siedentopf  and  Zsigmondy  in  Ger- 
many and  by  Cotton  and  Mouton  in  France.  In  this 


SUSPENSIONS.  39 

instrument  a  beam  of  strong  light  is  directed  through 
the  suspension,  so  that  its  particles  become  illuminated. 
They  are  then  observed  by  means  of  a  microscope  in  a 
direction  perpendicular  to  that  of  the  beam  of  light. 
In  this  manner  particles  of  not  more  than  0.000006 
mm.  may  be  detected,  when  they  are  illuminated  by 
solar  light.  If  the  total  quantity  of  suspended  matter 
is  known  and  the  number  of  particles  counted  the  mean 
diameter  of  each  particle  may  be  determined.  It  is 
usually  assumed  that  the  particles  are  of  a  spherical 
form. 

The  particles  may  be  of  still  smaller  dimensions  than 
0.000006  mm.  They  are  then  invisible  with  the 
strongest  illumination  which  we  can  produce.  Yet 
sometimes  even  then  a  weak  Tyndall-phenomenon  may 
be  observed. 

These  suspensions  are  often  called  sols.  In  many 
cases  the  suspended  particles  retain  with  remarkably 
strong  attraction  a  certain  quantity  of  the  solution  from 
which  they  were  precipitated.  This  is  for  instance  the 
case  with  iron  hydrate,  which  adsorbs  chlorine  ions 
from  the  surrounding  solution  of  FeCl3. 

The  suspended  particles  are  subject  to  the  Brownian 
movement  and  this  circumstance  causes  them  to  diffuse 
to  a  certain  extent.  If  the  particles  are  coarse  as  in 
the  cases  studied  by  Perrin,  their  concentration  was 
observed  to  decrease  very  rapidly  upwards.  Thus  their 
number  in  the  same  volume  decreased  to  one  half,  with 
an  increase  over  a  height  of  only  0.03  mm.  The 
diameter  of  the  particles  was  0.00042  mm.  In  a  height 
of  1  mm.  the  concentration  decreases  in  the  proportion 
of  about  ten  thousand  millions.  Hence  one  may  say 


40  THEORIES   OF   SOLUTIONS. 

that  the  main  amount  of  the  fluid  is  wholly  free  from 
these  particles.  But  smaller  particles  subside  very 
slowly  and  may  remain  suspended  in  the  fluid  for  an 
unlimited  time.  With  extremely  minute  particles  of 
gold  Svedberg  measured  the  diffusion  colorimetrically 
and  found  its  constant  at  17°  to  be  0.27  per  day, 
whereas  the  corresponding  constants  for  H2,  02,  C12, 
Br2  and  I2  in  water  were  3.75,  1.62,  1.22,  0.8  and 
0.5  respectively.  The  gold-emulsion  was  prepared 
according  to  a  method  given  by  Zsigmondy,  the  so- 
called  phosphorus-method.  Zsigmondy  estimates  the 
diameter  of  the  particles,  which  cannot  be  seen  with 
the  ultra-microscope,  to  be  a  millionth  millimeter, 
Svedberg  calculated  it  from  the  rate  of  diffusion  accord- 
ing to  a  formula  of  Einstein  to  the  magnitude  0.94 
millionths  of  a  millimeter.  The  corresponding  values 
for  H2,  02,  C12,  Br2  and  I2  are  according  to  the  formula  of 
Einstein  0.06,  0.20,  0.20,  0.32  and  0.52  respectively  in 
the  same  units.  Obviously  the  difference  from  a  real 
so  ution  is  in  this  case  not  very  great.  It  is  evident 
that  currents  produced  by  the  slightest  inequality  of 
temperature  may  disturb  these  observations. 

As  early  as  in  1809  Reuss  in  Moscow  observed  that 
small  suspended  particles  in  a  fluid  are  moved  by  an 
electric  current.  This  indicates  that  they  carry  a  cer- 
tain electric  charge.  The  surrounding  fluid  is  charged 
with  the  opposite  electricity  and  is  therefore  carried  in 
the  opposite  direction  by  the  current.  According  to  a 
rule  formulated  by  Coehn  the  substance  with  the 
greater  dielectric  constant  is  charged  positively.  Water 
has  a  higher  constant  than  most  other  substances  and 
is  therefore  generally  charged  positively  and  the 


SUSPENSIONS.  41 

suspended  particles  negatively.  Some  few  substances 
are  exceptions,  especially  oxides  such  as  those  of  iron, 
zinc,  cobalt  and  aluminium,  also  carbonate  of  baryta, 
hydroxides,  etc. 

If  we  have  water  in  a  narrow  glass  tube  with  two 
electrodes,  between  which  a  current  is  carried,  the 
water  is  carried  along  with  the  current.  The  same  is 
the  case  if  a  current  traverses  a  porous  diaphragm, 
which  may  be  regarded  as  a  system  of  capillary  tubes 
through  which  the  water  is  pressed.  This  curious 
phenomenon  was  observed  at  a  very  early  stage  as 
such  porous  diaphragms  are  used  in  galvanic  cells. 
The  strength  of  such  a  current  is  easily  measured  by 
means  of  the  height  to  which  the  fluid  can  be  pressed 
up  or  by  means  of  the  quantity  of  fluid  transported. 

The  velocity  with  which  suspended  particles  move 
under  the  influence  of  the  electric  current  is  propor- 
tional to  the  potential-gradient,  just  as  the  movement 
of  ions  is.  This  velocity  of  the  particles  is  therefore 
reduced  to  that  which  would  be  found  if  the  potential 
gradient  were  1  volt  per  cm.  There  have  been  found 
different  values  lying  between  about  10.10-5  and  40.1Q-5 
cm.  per  second,  about  the  same  as  for  ions.  (The  corre- 
sponding velocity  at  18°  C.  is  for  Li-ion  36. 10-5  for 
K-ion  66. 10-5). 

The  particles  are  charged  to  a  certain  potential  above 
or  below  that  of  the  surrounding  fluid.  It  is  of  the 
same  sign  as  the  charge  and  proportional  to  it  and 
inversely  proportional  to  the  radius  of  the  particle. 
This  potential  reaches  a  value  of  some  centi volts.  If 
now  the  radius  of  the  particle  is  doubled,  the  charge 
must  be  doubled  in  order  to  give  the  same  difference  of 


42  THEORIES   OF   SOLUTIONS. 

potential.  The  driving  force  is  (if  the  potential 
gradient  remains  constant)  proportional  to  the  charge, 
therefore  proportional  to  the  radius.  But  on  the  other 
hand  according  to  Stokes'  law  the  friction  increases 
proportionally  to  the  radius  and  the  velocity.  (Stokes' 
law  is  not  absolutely  exact  for  such  small  particles,  see 
p.  32 ).  Therefore  the  velocity  remains  the  same  inde- 
pendently of  the  radius  of  the  particle,  a  fact  which 
agrees  well  with  experiment.  On  this  ground  the 
velocity  would  remain  unaltered  if  the  dimensions  of 
the  particles  decreased  to  molecular  magnitude.  This 
circumstance,  combined  with  the  similar  magnitude  of 
the  mobility  of  ions  and  particles,  indicates  that  the 
suspended  particles  may  to  a  certain  degree  be  regarded 
as  ions  of  very  great  dimensions. 

Experiments  on  electric  endosmose  as  well  as  on  the 
electric  traction  of  suspended  particles  indicate  that 
the  charge  of  the  suspended  substance  is  in  a  high 
degree  dependent  on  electrolytes  present  in  the  water. 
Acids  and  bases  especially  exert  a  great  influence,  their 
hydrogen  or  hydroxyl  ions  being  adsorbed  by  the  solid 
particles.  As  the  latter  are  generally  negatively 
charged,  they  may  by  means  of  the  hydrogen  ions  be 
charged  positively,  so  that  the  direction  of  motion  of 
the  fluid  and  particles  is  changed.  The  influence  of 
the  ions  increases  with  the  quantity  of  acid  or  base 
added,  so  that  it  is  possible  to  gradually  alter  the 
charge  of  the  suspended  particles  or  of  the  diaphragm 
(in  osmotic  experiments)  from  negative  to  positive. 

Of  other  ions,  the  monovalent  ones  have  a  much 
smaller  effect  than  the  bivalent  ones,  the  latter  a 
smaller  effect  than  the  trivalent  ones.  The  suspended 


SUSPENSIONS.  43 

particle  adsorbs  with  preference  those  salt-ions  which 
have  a  charge  opposite  to  its  own.  Therefore  the 
movement  of  the  particles  is  generally  hampered  by 
addition  of  salts  and  especially  of  such  salts  as  possess 
polyvalent  ions  of  a  charge  opposite  to  that  of  the 
particle.  Sometimes  it  may  happen  that  in  such  cases 
the  final  total  charge  is  the  opposite  of  that  of  the 
particle  in  water  alone,  just  as  in  the  addition  of  acids. 
Thus  Burton  found  that  a  0.005  normal  solution  of 
A12(S04)3  was  sufficient  to  neutralize  the  negative  charge 
of  suspended  silver-particles,  so  that  in  higher  con- 
centrations of  the  aluminium-sulphate  the  silver-par- 
ticles migrated  in  the  direction  of  the  current. 

Electrolytes  have  another  influence  upon  suspensions. 
It  was  very  well  known  to  geologists  that  suspended 
particles  carried  out  into  the  sea  subside  much  more 
rapidly  in  salt  than  in  fresh  water.  Barus  investigated 
very  thoroughly  the  influence  of  different  substances 
and  showed  that  non-electrolytes  have  no  influence, 
acids  and  salts  of  heavy  metals  on  the  contrary  a  very 
great  one.  This  has  been  verified  by  Bodlaender  who 
found  that  with  kaoline-powder  in  water,  a  concentra- 
tion of  0.0001  normal  ZnS04  causes  subsidence  in  about 
the  same  degree  as  a  0.00015  normal  solution  of  sul- 
phuric acid  and  as  a  0.003  normal  solution  of  ammon- 
ium chloride.  Alkalis  have  hardly  any  action.  As  a 
general  rule  it  may  be  said  that  acids  and  polyvalent 
positive  ions  exert  the  greatest  action.  (The  rule  has 
some  very  peculiar  exceptions  in  phosphoric,  tartaric 
and  oxalic  acids,  but  not  in  the  very  much  weaker 
acetic  acid;  a  redetermination  seems  therefore  very 
desirable). 


44 


THEORIES   OF   SOLUTIONS. 


Similar  experiments  have  been  performed  by  Bech- 
hold  and  others.  The  former  found  that  the  following 
quantities  (in  equivalents)  of  different  electrolytes  exert 
the  same  action  in  precipitating  emulsions  of  mastich: 


HgCl2  oo 

KOH  oo 
NaCl  1000 
CHsCOOH  500 

Ag  NO8  125 

MgSO4  100 

MgN2O«  100 

ZnSO4  100 


CaCl2 

CaN2O6 

Ba(OH)2 

BaCl2 

BaN206 

ZnN2O6 

CoN206 

NiN2O6 


50  CdSO4  25    CuN2O6  5 

50  Ni(CH3C02)225     Cu(CH3C02)2  5 

50  HC1 

50  H2S04 

50  PtCl4 

50  CuCl2 


10  HgN03 

10  FeCl3 

10  FeN3O9 

10  A12(S04)3 


50    CuSO4 
50    PbN2O6 


10    A1N3O9 
5     Fe2(S04)3 


1.25 
1 
1 

0.5 
0.5 
0.5 


The  anions  seem  to  exert  a  very  insignificant  in- 
fluence. The  alkalis  have  no  influence  and  the  same 
holds  for  the  feebly  dissociated  mercuric  chloride  (a 
peculiar  case  since  HgNO3  has  a  very  strong  action). 
The  salts  of  monovalent  metals  act  much  less  than 
those  of  bivalent  metals,  to  which  silver  approaches 
very  closely.  A  still  more  powerful  action  is  character- 
istic of  the  strong  acids  (not  of  the  weak  acetic  acid). 
Some  few  nitrates  and  acetates  act  more  strongly  than 
even  the  strong  acids  and  by  far  the  greatest  action  is 
exerted  by  the  trivalent  positive  ions. 

Rather  many  irregularities,  which  still  await  their 
explanation,  are  found,  but  in  general  it  seems  as  if 
the  discharging  property  of  the  ions  had  the  greatest 
influence  on  the  negatively  charged  mastich-droplets. 

According  to  experiments  of  Whitney  and  Straw, 
the  hydroxyl-ions  seem  to  favor  the  suspension  of 
certain  substances,  such  as  turpentine,  carvene,  kaoline, 
soot  and  silver. 

Similar  experiments  have  been  carried  out  with  the 
negatively  charged  suspension  of  arsenious  sulphide. 


SUSPENSIONS.  45 

The  greatest  action  was  found  to  be  exerted  by  trivalent 
positive  ions,  an  intermediate  position  was  held  by 
divalent  and  the  weakest  action  was  due  to  monovalent 
positive  ions.  In  this  case  the  hydrogen  ions  did  not 
differ  so  very  much  from  potassium-,  sodium-  or 
lithium-ions.  On  the  other  hand  some  organic  positive 
ions  such  as  those  of  aniline,  toluidine,  morphium  and 
fuchsine  had  an  abnormally  great  action,  sometimes 
greater  than  that  of  divalent  ions.  Negative  ions  exert 
no  appreciable  influence. 

In  exactly  the  opposite  way  the  ions  react  with  a 
positively  charged  sol,  as  the  following  experiments  by 
Freundlich  on  Fe  (OH)3  suspension  indicate.  Hardly 
any  influence  at  all  was  exerted  by  hydrochloric  acid. 
The  quantities  of  different  salts  required  to  give  a 
precipitate  were  the  following  (in  millimoles  per  litre) : 

HCl    >  400  NaCl  9.25  MgSO4      0.217 

KI  16.2  KCL  9.03  K2SO4        0.204 

KBr  12.5  MBa(OH)20.42  K2Cr2O7     0.194 

KNO3         11.9*  H2SO4about0.5 

KBaCl2        9.64  T12SO4          0.219 

The  bases  (Ba02H2)  rank  here  with  the  salts  of 
divalent  anions  (S04  and  Cr207) ;  a  far  smaller  influence 
is  exerted  by  the  salts  of  monovalent  ions  and  the  mono- 
valent acids  give  an  exceptionally  low  effects  Also 
organic  anions  are  much  more  effective  than  inorganic 
ones,  according  to  Linder  and  Picton.  The  hydrogen 
ion  has  a  suspending  power  for  positively  charged 
suspensions. 

The  rule  of  the  greater  effectiveness  of  polyvalent  ions 
was  first  found  by  Schulze  in  1882;  his  experiments 
dealt  only  with  sols  of  A^Ss  and  Sb2S3;  but  this  rule 
has  been  verified  in  all  the  cases  thoroughly  examined 
by  the  following  investigators. 


46  THEOKIES  OF  SOLUTIONS. 

The  chemical  behavior  of  suspended  particles  of 
noble  metals  was  very  thoroughly  examined  by  Sved- 
berg  and  his  pupils.  Just  as  spongy  platinum  destroys 
hydrogen  peroxide,  so  platinum  sol  has  the  same  effect, 
but  in  a  still  higher  degree  corresponding  to  its  fine 
division. 

Bredig  and  Mueller  von  Berneck  shook  together 
fulminating  gas  and  2.5  c.c.  water  containing  about  0.17 
milligrams  of  suspended  platinum  and  found  that  the 
reaction  went  on  with  constant  velocity,  as  was  quite 
natural,  since  the  concentration  of  fulminating  gas 
always  remained  the  same  throughout  the  shaking. 
The  combined  quantities  are  seen  hi  the  following 
figures  (valid  at  25°  C.) : 

Time  Minute*.  Combined  Gas  c.o.  Velocity  c.c.  per  Min. 
10                              17.8  1.78 

20  35.8  1.80 

30  54.8  1.90 

40  72.4  1.76 

50  90.2  1.78 

After  two  weeks,  during  which  this  liquid  had  been 
shaken  in  the  day-tune  with  a  total  resulting  combina- 
tion of  about  10,000  c.c.  of  fulminating  gas,  it  was  tried 
again  and  found  to  cause  98.2  c.c.  of  fulminating  gas 
to  combine  in  50  minutes.  The  effectiveness  of  the 
platinum-sol  had  therefore  not  diminished. 

They  then  investigated  the  decomposition  of  hydro- 
gen peroxide  hi  neutral  or  weakly  acid  (through  an 
addition  of  srVff  c-c-  NaH2P04)  solution.  They  found 
that  the  reaction  was  of  the  monomolecular  type,  i.  e., 
that  the  quantity  of  H2O2  decomposed  per  minute  was 
proportional  to  the  concentration  of  H202,  as  was  to  be 
expected. 


SUSPENSIONS.  47 

A  totally  different  set  of  relations  is  obtained  if 
sodium  hydrate  is  added.  With  increasing  quantity 
of  the  hydrate  the  velocity  of  reaction  at  first  increases, 
then  reaches  a  maximum  when  the  solution  is  about 
0.02  normal  in  regard  to  the  alkali,  and  afterwards  it 
decreases  again  if  the  concentration  of  the  latter  is 
further  increased.  This  is  evident  from  the  following 
figures,  which  indicate  the  time  which  is  necessary  for 
decomposition  of  -fa  normal  H202  to  its  half  strength. 
The  quantity  of  platinum  was  always  the  same,  ^WirTfTF 
normal. 

Cone,  of  NaOH.        0  1/512  1/256  1/128  1/64  1/32  1/16  1/8  1/4  1/2      1 
Time  in  minutes    255       34       28       24     25     22     34  34  70162520 

Here  the  rate  of  decomposition  is  for  low  concentra- 
tions of  NaOH  almost  independent  of  the  concentration 
of  H2O2,  whereas  at  higher  concentrations  of  NaOH  the 
reaction  follows  the  monomolecular  formula,  i.  e.t  the 
rate  is  proportional  to  the  concentration  of  H202  as  is 
seen  from  the  following  figures  (valid  at  25°  C.). 

1/512  »  NaOH. 

Time.  a — z                             *t  k0 

0  23.9  — 

6  22.4  0.0047  0.25 

15  19.65  0.0057  0.28 

25  16.5  0.0064  0.30 

40  11.17  0.0083  0.32 

55                      6.35  0.0105  0.32 

1/128 n  NaOH. 

Time.  a— *                             *x  *0 

0  23.83 

6  21.15  0.0086  0.45 

15  16.67  0.0104  0.48 

25  11.6  0.0125  0.49 

40  5.33  0.0153  0.46 


48  THEORIES   OF   SOLUTIONS. 

1/32  n  NaOH. 

Time.  a—x  k^  k0 

0  23.9 

6  20.02  0.0128  0.65 

15  15.4  0.0127  0.57 

25  10.9  0.0136  0.52 

40         6.13  0.0148  0.44 

a-x  is  the  quantity  of  H202  present,  determined  by 
titration.  fc  is  the  constant  giving  the  velocity  of 
reaction  according  to  the  monomolecular  formula,  kQ 
on  the  other  hand  the  velocity  of  reaction,  calculated 
on  the  supposition  of  a  constant  rate  from  the  beginning. 

In  the  first  instance  (1/512  n  NaOH)  &i  increases  in 
the  proportion  1  to  2.25  during  the  time  of  reaction. 
Even  the  quantity  kQ  is  not  absolutely  constant,  but 
shows  an  obvious  tendency  to  increase  with  time.  The 
second  case  (1/128  n  NaOH)  gives  almost  the  same 
behaviour,  but  kQ  is  very  nearly  constant.  In  the  third 
instance  ki  increases  slightly  (about  15  per  cent.)  with 
time,  so  that  the  reaction  proceeds  almost  as  a  mono- 
molecular  one;  on  the  other  hand  kQ  decreases  by  about 
a  third  of  its  original  value. 

Similar  irregularities  are  often  found  in  the  investiga- 
tion of  the  catalytic  action  of  ferments;  and  therefore 
Bredig  calls  platinum-sol  and  similar  substances  inor- 
ganic ferments.  A  maximum  effect  in  the  presence  of 
a  certain  quantity  of  sodium  hydrate  has  been  observed 
by  Jacobson  for  the  decomposition  of  H202  by  means 
of  emulsin,  pancreatic  juice  and  malt-ferment.  In  the 
inversion  of  cane-sugar  by  means  of  invertin  the  maxi- 
mum effect  is  attained  if  a  certain  quantity  of  acid  is 
present.  In  this  case  also  the  quantity  of  cane  sugar 
decomposed  in  unit  time  is  nearly  independent  of  the 
concentration  of  the  sugar,  if  this  exceeds  2  per  cent., 


SUSPENSIONS.  49 

but  at  very  low  concentration  (below  0.5  per  cent.)  the 
rate  of  inversion  follows  the  monomolecular  formula. 

The  similarity  between  ferments  and  platinum-sol  is 
still  more  strikingly  manifested  in  the  fact  that  in  each 
case  their  action  is  paralysed  by  the  presence  of  very 
small  quantities  of  " poisons."  Hydrocyanic  acid,  car- 
bon monoxide,  iodine,  mercuric  chloride,  hydrogen  sul- 
phide, etc.,  exert  such  an  action  on  platinum-sol. 
The  first-mentioned  has  a  very  peculiar  action;  at 
first  it  paralyses  the  sol,  but  later  on  this  recovers  and 
has  an  even  greater  effect  than  without  the  poison. 
A  similar  recovery  of  emulsin  and  of  pancreatic 
ferment  after  their  paralysis  by  HCN  has  been  observed 
by  Jacobson. 

In  these  changes,  the  reacting  substances  probably 
condense  upon  the  finely  divided  metallic  particles,  as 
we  shall  see  in  the  next  chapter,  and  in  such  condensed 
systems  the  chief  reaction  takes  place.  This  is  prob- 
ably the  case  with  many  gas-reactions  in  the  presence 
of  finely  divided  platinum,  for  instance,  the  oxidation 
of  S02  by  means  of  oxygen  to  S03,  which  has  been 
examined  by  Fink.  Wallach  found  that  the  terpenes 
and  their  derivatives  may  easily  give  addition-products 
with  hydrogen  in  the  presence  of  finely  divided  pal- 
ladium, prepared  according  to  Bredig's  method  (cf. 
next  chapter),  which  is  known  to  condense  hydrogen  on 
its  surface  very  strongly.  Evidently  the  organic  sub- 
stances are  also  concentrated  around  the  palladium 
particles  and  in  these  surface-layers  the  reaction  takes 
place.  These  reactions  proceed  just  as  if  the  reagents 
were  subjected  to  a  high  pressure,  which  is  also  favor- 
able to  them 

5 


50  THEORIES   OF   SOLUTIONS. 

The  magnitude  of  the  suspended  particles  is  highly 
dependent  upon  the  concentration  of  the  solutions  from 
which  they  are  precipitated,  as  Biltz  in  particular  has 
proved.  On  this  magnitude  the  optical  properties  of 
the  suspension,  color  and  translucence,  which  are 
caused  by  diffraction  of  the  light,  depend.  Thus 
Schulze  as  early  as  1882  observed  that  if  he  prepared 
two  suspensions  of  A^Ss  the  one  from  a  concentrated, 
the  other  from  a  dilute  solution  of  As203  by  leading  in 
H2S  (cf.  p.  36),  and  then  diluted  the  former  until  the 
concentration  of  As20a  was  the  same  as  in  the  latter, 
the  suspension  containing  the  coarser  particles  were 
less  translucent  and  possessed  a  clearer  yellow  colour, 
than  the  yellowish  red  suspension  of  finer  particles. 
Svedberg  subjected  this  peculiarity  to  a  closer  investi- 
gation. He  used,  for  instance,  the  method  of  reducing 
gold  from  its  chloride  by  means  of  chlorhydrate  of 
hydrazin  and  obtained  the  figures  given  hi  the  following 
table,  where  c  is  the  concentration  (normality)  of  the 
solution  of  gold  chloride  (AuCl3)  used  and  k  the  depth  of 
its  colour  determined  by  dilution  until  the  colour  was  not 
longer  perceptible. 

m  Colour 

343  bluish  grey, 

blue, 
blue, 
37 

fuchsin  red. 
20 


c 

1 

50,000  X  10-7 

2,000 

21,000 

5,000 

10,000 

75,000 

7,500 

200,000 

6,000 

250,000 

3,300 

200,000 

1,700 

125,000 

1,000 

100,000 

500 

200 

50,000 

15 

17,000 

7 

25,000 

13 

M 


SUSPENSIONS.  51 

The  intensity  k  of  the  colour  of  solutions  containing 
the  same  quantity  of  gold  at  first  increases  when  the 
gold  particles  diminish  and  thereafter  decreases.  The 
diameter  of  the  particles,  in  millionths  of  a  miUimeter 
is  tabulated  under  m\  it  diminishes  rapidly  with  c,  and 
at  the  same  tune  the  colour  changes.  Emulsions  con- 
taining still  smaller  particles  of  gold  reduced  by  means 
of  an  ethereal  solution  of  phosphorus  (Zsigmondy's 
method)  are  ruby  red  to  reddish  yellow  according 
to  the  fineness  of  the  particles.  This  last  column 
reminds  one  of  that  of  gold  chloride,  which  has  a  value 
of  A:  =  5,000.  Similar  maxima  of  k  although  not  so 
strongly  marked  have  been  obtained  by  Svedberg  for 
suspensions  of  Fe(OH)3  and  of  As2S3. 

If  a  solution  of  phenol  in  water  is  cooled,  droplets 
of  phenol  separate  out  and  two  coexisting  phases  are 
formed.  Similarly  when  a  solution  of  gelatine  is 
cooled  it  gives  a  solid  jelly  which  after  all  consists  of 
two  different  phases,  one  of  gelatine  with  a  small  per- 
centage of  water  and  one  of  water  with  a  small  content 
of  gelatine,  as  Buetschli  at  first  demonstrated  as  prob- 
able. 

Similar  properties  are  found  with  some  emulsions,  and 
especially  with  those  of  sulphur  prepared  according 
to  Rappo  by  allowing  a  saturated  solution  of  sodium 
thiosulphate  to  drop  into  cold  concentrated  sulphuric 
acid.  Rappo  found  that  this  emulsion  is  precipitated  by 
the  addition  of  certain  salts  such  as  NaCl,  KN03,  KC1, 
Na2  S04  or  K2S04,  although  NH4-salts  do  not  seem  to 
possess  this  power.  The  precipitates  made  by  means 
of  sodium  salts,  dissolve  in  increased  quantities  of 
water  or  at  higher  temperatures. 


52  THEORIES   OF   SOLUTIONS. 

Svedberg  and  his  pupil  Oden  investigated  this  phe- 
nomenon. They  found  that  the  solubility  of  this 
sulphur  increased  with  temperature  approximately 
according  to  an  exponential  law,  which  holds  good  also 
for  the  change  of  solubility  of  other  substances  with 
temperature.  From  this  it  is  possible  to  calculate  the 
heat  of  solution  of  the  sulphur  (cfr.  Lecture  V)  and  in 
this  manner  I  have  found  the  following  values  per 
grammolecule: 

Normal  Cal.  Solubility  at  20° 

in  0.2  NaCl  42,400  (between  14.8°  and  25.0°)  14.1% 

in  0.3  NaCl  22,000  (between  16.5°  and  38.5°)    1.2 

in  0.4  NaCl  33,100  (between  23.1°  and  47.5°)    0.3 

in  0.5  NaCl  33,400  (between  31.9°  and  41.8°)    0.08 

in  0.2  NaBr  36,600  (between  14.9°  and  19.7°)  11.0 
in  0.2  (mol.)  Na«S04  42,500  (between  13.9°  and  22.6°)    4.1 

The  experimental  errors  are  very  great,  so  that  the 
calculated  values  of  the  heat  of  solution  may  be  regarded 
as  agreeing  rather  well  with  the  mean  value  36,200  cal., 
an  unusually  high  value  for  a  heat  of  solution. 

The  figures  giving  the  solubility  at  20°  indicate 
that  NaCl  and  NaBr  have  nearly  the  same  influence 
on  the  colloidal  sulphur,  while  Na^SOd  has  a  greater 
influence  than  NaCl  if  in  equimolecular,  but  less  in- 
fluence if  in  equivalent  solution. 

Oden  has  investigated  this  last  property  more  fully. 
He  finds  that  different  preparations  of  suspended 
sulphur  behave  rather  differently,  and  this  explains 
the  irregularity  in  Svedberg's  figures.  He  finds  that 
if  the  solubility  of  the  sulphur  (in  per  cent.)  at  16°  C. 
is  represented  by  S  and  the  normality  of  the  NaCl  by  n 
then  the  following  experimental  formula  holds  good: 

S  =  32,810 


SUSPENSIONS. 


53 


as  is  seen  from  the  following  figures: 


0.21 

0.34 
0.46 
0.58 
0.74 


6'obg. 

5.43 
1.68 
0.74 
0.36 
0.07 


Scale. 
6.51 
1.69 
0.73 
0.38 
0.19 


Diff. 
-1.08 
—0.01 
+0.01 
-0.02 
-0.12 


Different  salts  have  very  different  powers  of  causing 
precipitates.  The  following  figures  give  the  inverse 
values  of  the  quantities  in  gram  equivalents  per  liter, 
which  must  be  added  in  order  to  produce  precipitation. 
The  solutions  lose  their  transparency  at  a  certain 
concentration,  which  may  be  determined  rather  ac- 
curately. The  inverse  value  of  their  concentration  in 
gram  equivalents  per  litre  is  given  below : 


LiCl 

1.1 

KC1 

47.5 

MgS04 

54 

ZnS04 

6.6 

NILCl 

2.3 

K2S04 

39.7 

MgN206 

63 

CdN20« 

10.2 

(NEU)2S04 

1.7 

KNO, 

45.5 

CaCl2 

123 

A1C1. 

76 

NH4NOs 

2.0 

RbCl 

63 

CaN20« 

124 

CuSO4 

51 

NaCl 

6.1 

CsCl 

108 

SrN20« 

193 

MnN2O« 

53 

Na2S04 

5.7 

BaCl2 

238 

NiN206 

11.2 

NaNO, 

6.1 

BaN206 

231 

UO2N2O6 

36.5 

An  addition  of  acids  increases  the  stability  of  the 
suspension,  so  that  much  greater  concentrations  of  the 
salts  are  needed  in  order  to  produce  precipitation,  than 
if  the  acid  is  not  present.  HN03  and  H2S04  have  the 
greatest  influence,  HC1  and  HBr  much  less,  about  60 
per  cent,  of  that  of  HNO3  or  H2SO4  in  equimolecular 
solution.  This  so-called  dispersing  action  increases  till 
it  reaches  a  maximum  at  a  certain  concentration  and 
thereafter  it  diminishes  again.  Formic  acid  has  about 
14  times  less  action  than  HN03  or  H2S04  in  concentra- 
tions below  normal.  It  does  not  possess  a  maximum 


54  THEORIES  OF  SOLUTIONS. 

of  action  at  any  concentration.    Acetic  acid  possesses 
a  very  small  activity  in  this  respect. 

It  seems  very  difficult  to  draw  general  conclusions 
from  all  these  figures.  In  groups  of  similar  salts,  as 
for  instance  the  salts  of  the  alkali-metals,  the  precipitat- 
ing influence  of  the  salt  increases  very  rapidly  with  the 
atomic  weight  of  the  metal,  and  metals  of  a  high 
valency  generally  have  a  greater  influence,  but  the 
regularity  is  not  very  pronounced. 


LECTURE  IV. 

THE  PHENOMENA  OF  ADSORPTION. 

IN  the  year  1777  two  chemists,  the  German,  R. 
Scheele  and  the  Italian,  F.  Fontana  independently 
discovered  that  charcoal  has  a  great  tendency  to  take 
up  and  retain  gases  from  its  surroundings.  This  phe- 
nomenon was  then  studied  by  a  great  number  of 
scientists,  amongst  whom  the  renowned  French  savant 
Saussure  (1814)  deserves  special  mention.  In  1791 
Lowitz  found  that  charcoal  is  also  able  to  take  up 
coloring  matter  from  solutions,  so  that  a  complete 
decoloration  of  fluids  could  be  brought  about  by  simply 
filtering  them  through  carbon,  a  method  which  is  of 
the  greatest  value  for  many  industrial  processes. 
Payen  afterwards  showed  that  a  great  number  of  salts 
and  other  substances  were  condensed  upon  charcoal. 
In  further  investigations  it  was  discovered  that  not 
only  carbon  but  even  other  substances,  which  are  finely 
divided  or  consist  of  agglomerations  of  fine  fibres,  such 
as  finely  divided  platinum,  iridium,  powdered  glass  or 
glass-wool,  powdered  silicic  acid,  clay,  kaoline,  metastan- 
nic  acid,  meerschaum,  asbestos,  paper,  cotton,  leather, 
silk  or  wool  possess  the  same  attracting  or  condensing 
power  as  charcoal. 

On  this  property  of  fibres  of  mineral,  vegetable,  or 
animal  origin  many  dyeing  and  tanning  processes  de- 
pend; further  the  retention  of  carbonic  acid,  moisture 
and  salts  necessary  for  the  vegetation  in  different  soils 

65 


56  THEORIES  OF  SOLUTIONS. 

as  well  as  the  hygroscopic  nature  of  various  materials 
are  consequences  of  adsorption  processes.  Clearly  they 
are  of  the  greatest  practical  importance  and  they  have 
therefore  attracted  the  keen  interest  of  many  investi- 
gators. 

The  chief  problem,  which  these  investigators  have 
had  in  view,  was  to  determine  how  great  the  quantity 
taken  up  by  the  porous  substance  was,  and  how  it 
changed  with  the  concentration  of  the  surrounding  gas 
or  solution  and  with  the  temperature.  The  phenome- 
non itself  is  according  to  a  suggestion  by  E.  du  Bois 
Reymond  called  " adsorption,"  which  is  meant  to 
indicate  that  the  " adsorbed"  substance  does  not  enter 
into  the  interior  of  the  " adsorbent,"  but  is  only  at- 
tracted to  its  surface,  in  contradistinction  to  solution 
(especially  solid  solution)  or  chemical  interaction. 
These  two  latter  processes  sometimes  accompany  ad- 
sorption and  so  exert  a  disturbing  influence. 

It  was  found,  as  one  would  expect,  that  the  adsorbed 
quantity  increases  with  the  concentration  of  the  sur- 
rounding gas  or  solution.  In  some  cases  there  exists  a 
proportionality,  reminding  one  of  the  law  of  Henry,  for 
instance,  with  gases  in  general  at  high  temperatures 
and  with  hydrogen  and  helium  even  at  rather  low  tem- 
peratures (  —  80°  C.).  But  in  the  majority  of  cases  the 
adsorbed  quantity  increases  much  more  slowly  than  the 
concentration  considered,  and  this  was  expressed  by 
means  of  a  formula,  which  has  often  proved  very  useful 
in  interpolations,  namely, 

a  =  kcn, 
where  a  is  the  adsorbed  quantity  per  g.  of  adsorbent,  k 


THE   PHENOMENA   OF  ADSORPTION.  57 

a  constant  (the  adsorption  constant),  c  the  pressure  of 
the  surrounding  gas  or  the  concentration  of  the  sur- 
rounding liquid  studied  and  finally  n  is  an  exponent 
less  than  unity. 
The  formula  was  controlled  by  giving  it  the  form 

log  a  =  log  k  +  n  log  c 

and  plotting  log  a  against  log  c  as  abscissa.  The  points 
thus  determined  were  joined  together  by  a  curve,  which 
ought  to  be  a  straight  line  if  n  is  constant,  as  it  was 
generally  found  to  be  (cf.  diagram  p.  66).  As  examples 
the  following  figures  may  be  given: 

ADSORPTION  OP  CARBONIC  ACID  ON  CHARCOAL  AT  0.°  n  =  0.333; 

k  =  2.96  (Travers). 

c                                      a  (observed).  a  (calculated). 

0.41                                     1.94  2.21 

2.51                                   3.94  3.99 

13.74                                   7.65  7.00 

41.64                                   10.49  10.1 

85.86                                   12.97  12.9 

Here,  as  is  usually  the  case  with  gases,  the  concentra- 
tion is  expressed  as  gas-pressure  in  cm.  of  mercury; 
a  in  cubic  centimeters  (at  0°,  and  76  cm.)  of  the  adsorbed 
gas  on  one  gram  of  the  adsorbing  substance.  In  this 
case  the  value  of  a  at  low  pressures  falls  a  little  short 
of  the  calculation,  i.  e.y  the  straight  line  is  bent  down 
somewhat  towards  the  abscissa  axis.  This  phenomenon 
is  general  with  gases  at  low  pressures. 

ADSORPTION  OF  ACETIC  ACID  ON  CHARCOAL  AT  14°  n  -  0.25; 
k  =  2.112  (G.  C.  Schmidt). 

o  a  (observed).  a  (calculated). 

0.0365  0.93  0.923 

0.084  1.15  1.137 

0.135  1.248  1.282 

0.206  1.43  1.423 

0.350  1.62  1.625 


58  THEORIES  OF  SOLUTIONS. 

The  agreement  between  the  observed  and  the  calcu- 
lated values  is  in  this  case  very  good.  Many  similar 
cases  were  investigated  and  on  the  whole  it  may  be 
said  that  the  calculated  values  were  in  good  accord 
with  the  observed  ones.  It  was  therefore  generally 
assumed  that  the  equation  above  represents  the  adsorp- 
tion phenomenon  at  constant  temperature,  i.  e.,  gives 
the  so-called  adsorption-isotherm.  As  will  be  seen 
later  on,  this  hypothesis  is  rather  far  from  the  truth, 
and  when  we  look  critically  at  the  tabulated  observa- 
tions we  find  in  most  cases,  that  the  intervals  in  which 
the  values  of  a  have  changed  are  very  limited,  as  for 
example,  hi  the  last  case  between  0.93  and  1.62,  i.  e., 
not  fully  hi  the  proportion  1  to  2. 

With  regard  to  the  influence  of  temperature,  it  was 
found  to  be  rather  insignificant  for  the  adsorption  of 
substances  from  their  solutions  especially  at  higher 
temperatures,  as  Freundlich  showed.  With  gases  the 
constant  k  decreased  exponentially  with  increasing  tem- 
perature and  n  increased  with  temperature  in  the  man- 
ner indicated  by  the  following  figures  for  the  adsorption 
of  carbonic  acid  on  charcoal  according  to  Travers's 
measurements. 

t  A- (observed).  k  (calculated).  n 

-  78°  14.29  16.62  0.133 

0°  2.96  2.96  0.333 

35°         1.236        1.364  0.461 

61°         0.721        0.768  0.479 

100°         0.324        0.324  0.518 

The  calculated  values  of  k  are  found  by  means  of 
the  following  formula: 

log  kt  =  log  k0  -  0.009608  t 

where  i  is  the  temperature  in  centrigade  degrees  and 
the  logarithms  are  to  the  base  10. 


THE   PHENOMENA   OF  ADSORPTION.  59 

If  the  temperature  were  increased  sufficiently  n  would 
approach  very  near  to  1;  on  the  other  hand  at  very 
low  temperatures  approaching  to  absolute  zero  n  takes 
values  decreasing  very  nearly  to  0. 

The  exponential  formula  given  above  indicates  that 
the  adsorbed  quantity  should  increase  to  infinity  if  the 
pressure  or  osmotic  pressure  of  the  examined  substances 
were  to  increase  without  limit.  This  was  also  believed 
to  be  the  case  until  quite  recently  G.  C.  Schmidt  found 
some  cases  (adsorption  of  acetic  acid  or  of  iodine  on 
carbon)  in  which  the  adsorption  reached  a  very  well 
marked  maximum,  S,  which  was  arrived  at  asymptot- 
ically on  increasing  the  concentration,  and  which  could 
therefore  not  be  exceeded. 

He  therefore  proposed  a  new  formula  of  the  type 


where  &,  A  and  S  are  constants.  This  formula  has  the 
weakness  that  it  contains  three  constants  to  be  deter- 
mined experimentally,  and  this  gives  it  only  the  value 
of  an  interpolation  formula  which  may  lack  a  higher 
physical  meaning.  If  a  approaches  very  near  to  S  we 
find  that  the  logarithmic  term  increases  very  rapidly 
towards  infinity,  i.  e.,  c  must  also  approach  infinity,  i.  e., 
S  is  a,  maximal  value  of  a. 

It  would  increase  the  value  of  the  formula  to  a  high 
degree  if  A  were  zero  or  if  it  were  a  function  of  S,  for 
then  there  would  be  only  two  constants  and  the  formula 
might  be  more  a  rational  one.  Schmidt  soon  found 
that  A  was  not  zero  and  therefore  determined  it  experi- 
mentally. On  inspecting  the  values  of  A  determined 


60 


THEORIES   OF   SOLUTIONS. 


by  Schmidt  I  was  surprised  to  see  that  the  product 
AS  was  very  nearly  a  constant  namely,  0.4343,  the 
ratio  between  common  and  natural  logarithms.  In  gen- 
eral it  was  a  trifle  lower,  as  is  indicated  by  the  following 
values  of  S  and  A  given  by  Schmidt. 

8A  System 

0.484  Acetic  acid,  charcoal 
from  cane  sugar. 

0.414  Acetic  acid,  charcoal  of 
animal  origin. 

0.4453  Iodine  in  benzene,  char- 
coal of  animal  origin. 

0.4218  Acetic  acid,  charcoal 
from  cane  sugar. 

0.3570  Acetic  acid,  charcoal  of 
animal  origin. 

0.4057  Acetic  acid,  charcoal 
from  cane  sugar. 

I  therefore  recalculated  Schmidt's  figures  under  the 
supposition  that  the  product  SA  was  really  0.4343  and 
found  for  instance  the  following  results  for  Schmidt's 
Tab.  12,  which  may  also  give  an  insight  into  the  real 
meaning  of  an  upper  limit  to  the  adsorbed  quantity. 

SCHMIDT'S  TAB.  12  100  c.c.  ACETIC  ACID  WITH  10  g. 

CHARCOAL  FROM   CANE   SUGAR.      S  =  0.905. 


Schmidt's  Tab.    8 

s 
gives  0.88 

A 

0.55 

Tab.    9 

"     2.48 

0.1670 

"     10 

"     1.36 

0.3275 

"    12 

"     0.9052 

0.4660 

"    14 

"     1.4570 

0.245 

"    16 

"     1.7829 

0.2276 

0.00884 

0.03217 

0.0372 

0.2116 

1.161 

3.759 

3.752 

5.602 

9.175 

16.60 

29.38 

30.6 


0.05223 

0.1006 

0.1259 

0.3224 

0.5879 

0.7952 

0.8105 

0.8284 

0.901 

0.905 

0.902 

0.904 


k 

12.60 
11.90 
8.65 
5.81 
6.87 
7.05 
6.34 
8.33 
4.77 


THE   PHENOMENA  OF  ADSORPTION.  61 

As  is  seen  from  the  figures  at  the  bottom  of  the  table 
a  increases  very  slowly  with  increase  of  c,  after  the  latter 
has  reached  a  value  higher  than  0.9  (grams  per  100  c.c.). 
The  three  last  figures  for  a  are  to  be  regarded  as  con- 
stant within  the  errors  of  observation.  Schmidt  there- 
fore took  a  mean  value  of  those  and  some  other  figures 
0.905  (g  in  10  g  carbon.)  as  giving  the  limiting  value 
which  the  adsorption  of  acetic  acid  might  reach  in 
solutions  as  highly  concentrated  as  possible. 

The  value  under  k  should  be  a  constant,  whereas 
it  in  reality  changes  in  about  the  proportion  1  to  2. 
But  as  a  matter  of  fact  these  discrepancies  are  rather 
insignificant.  As  regards  the  end  value  4.77,  the  cor- 
responding value  of  a  (0.901)  lies  so  very  near  to  the 
limit  value  S  (0.905)  that  an  error  in  either  of  these 
values  of  0.004,  which  might  well  occur  would  render 
k  infinite.  The  second  and  the  third  observations  lie 
very  near  to  each  other  (in  regard  to  the  value  of  c) 
and  ought  to  approximately  give  the  same  value  of  k. 
But  for  these  weak  concentrations  again,  a  small 
experimental  error  gives  a  very  great  error  in  k.  The 
third  experiment  gives  very  nearly  the  right  value  of 
/c,  i.  e.,  about  the  average  one.  We  therefore  conclude 
that  A:  is  a  constant  within  the  limits  of  the  experi- 
mental errors.  As  will  be  seen  later  on  it  is  very 
probable  that  the  fc-values  increase  somewhat  with 
dilution  just  as  in  the  case  cited  here. 

The  equation  of  Schmidt  with  AS  =  0.4343  corre- 
sponds to  a  very  simple  differential  equation,  namely, 
da  =  1  S  -  a 
dc  ~~  k     a 
This  means  that  if  we  have  a  solution  of  the  concentra- 


62  THEORIES  OF  SOLUTIONS. 

tion  c  in  equilibrium  with  charcoal  every  10  grams  of 
which  carry  a  grams  of  solute  and  if  we  then  increase 
the  concentration  by  dcy  it  is  sufficient  to  add  a  quantity 
da  to  the  adsorbed  layer  in  order  that  the  equilibrium 
should  be  maintained.  The  equation  denotes  that  da 
is  zero,  when  S  =  a,  i.  e.,  the  limiting  adsorption  has 
been  attained.  It  also  denotes  that  do/dc  is  infinite  for 
a  =  0,  i.  e.,  that  on  the  addition  of  a  small  quantity  of 
dissolved  substance  to  pure  water  and  pure  charcoal, 
the  latter  takes  away  all  the  acetic  acid  from  the  solu- 
tion. We  also  see  from  the  figures  above  how  c  in- 
creases hi  a  ratio  nearly  proportional  to  the  square  of 
the  ratio  in  which  a  simultaneously  increases.  From  this 
it  follows  that  c:  a  at  infinite  dilution  is  zero,  as  is  shown 
by  the  differential  equation.  This  corresponds  also 
to  the  well-known  fact,  that  on  filtering  dissolved  dyes 
through  charcoal,  all  the  color  is  taken  away  at  once, 
a  fact  which  is  used  in  practice  for  purifying  solutions, 
e.  g.,  of  cane  sugar,  etc.  The  analogous  fact  that  at 
low  temperatures  charcoal  adsorbs  all  of  a  surrounding 
gas  is  well  known;  it  is  to  the  great  credit  of  Sir  James 
Dewar  that  he  has  introduced  this  very  convenient 
method  of  preparing  high  vacua. 

As  I  had  convinced  myself  that  the  new,  highly 
accurate  measurements  of  G.  C.  Schmidt  agree  very 
well  within  the  errors  of  observation  with  the  equation 
given  above,  I  enquired  next  as  to  how  gases  would 
behave.  From  older  investigations  it  was  perfectly 
clear  that  they  would  not  follow  the  equation  in  ques- 
tion at  high  temperatures. 

Now  there  have  appeared  during  the  past  year  two 
very  accurate  series  of  measurements  on  the  adsorption 


THE  PHENOMENA  OF  ADSORPTION.  63 

of  gases,  carried  out  by  the  Russian  Titoff  and  by  Miss 
Ida  Homfray,  who  worked  in  the  laboratory  of  Sir 
William  Ramsay.  It  seemed  very  probable  from  what 
they  had  said  regarding  their  observations,  that  they 
had  also  observed  a  maximum  charge  S  for  gases,  al- 
though they  had  not  given  such  an  explanation  to  their 
results.  Titoff  says,  that  at  high  charges  of  the  carbon 
there  comes  a  point  where  c  increases  with  extreme  rapid- 
ity as  compared  with  a.  For  carbonic  acid  and  am- 
monia at  —  76.5  and  —  23°.5  he  observed  values  of  a 
amounting  to  114.1  and  154.4  c.c.  per  g.  carbon,  respec- 
tively, whereas  according  to  the  formula  given  above, 
I  calculated  the  limiting  values  S  =  114.6  and  158,  re- 
spectively. Titoff  had  then  practically  reached  this 
limit,  especially  in  the  case  of  carbonic  acid. 

As  is  seen  from  my  calculations,  the  limiting  value 
of  S  is  independent  of  temperature  and  may  therefore 
be  called  the  constant  of  saturation.  For  carbonic  acid 
Titoff  has  given  two  series  of  observations  at  0°,  which 
I  quote  here  calculated  according  to  the  same  formula 
as  was  used  for  the  solutions,  c  is  expressed  as  pressure 
in  cm.  Hg. 


CARBONIC  ACID 

AT  0°  ADSORBED  BY  COCOANUT-CHARCOAL,  ACCORD- 

ING TO  TlTOFP. 

c 

a 

k 

0.05 

0.8491 

24.9 

0.32 

3.4601 

159 

1.09 

8.5059 

89 

2.54 

15.148 

60.5 

8.30 

27.782 

52.0 

17.35 

39.898 

48.9 

31.59 

50.241 

52.7 

45.42 

56.818 

56.0 

58.91 

61.372 

58.9 

70.32 

64.529 

61.6 

75.51 

65.854 

62.2 

64  THEORIES   OF   SOLUTIONS. 

Regarding  the  first  two  observations  Titoff  says  himself 
that  measurements  in  which  c  is  less  than  one,  are  very 
unreliable.  We  therefore  find  here  the  two  extreme 
values  of  k.  By  a  chance  their  geometrical  mean, 
about  63,  is  very  near  to  the  mean  value  of  k.  There- 
after k  is  nearly  constant,  sinking  a  little  to  begin  with, 
and  then  increasing  again.  This  last  increase  may  be 
due  to  a  small  inaccuracy  in  the  value  of  S  and  is 
therefore  not  of  much  importance,  but  the  decrease  of 
k  at  the  beginning  of  the  series  is  characteristic  and 
agrees  with  the  experiments  of  Schmidt. 

I  also  succeeded  in  calculating  the  figures  of  Miss 
Homfray  in  the  same  manner  and  give  below  the 
experimental  results  of  a  series  of  investigations  regard- 
ing methane. 

METHANE  AT  -33°  ADSORBED  BY  COCOANUT-COAL,  ACCORDING  TO 
Miss  HOMFRAY,  S  =  274. 

c  a  k 

0.45  35.21  140.6 

0.66  44.64  101.5 

0.94  55.36  89.5 

1.28  64.65  88.0 

1.65  73.80  85.1 

2.13  83.20  83.9 

2.68  92.12  84.0 

3.37  100.9  84.9 

4.10  109.5  85.3 

This  series  shows  a  high  degree  of  regularity,  which  is 
partially  explained  by  the  relatively  small  variation  of 
c.  It  gives  occasion  for  similar  remarks  concerning 
the  variation  of  the  constant  k  as  did  the  carbonic 
acid  series  of  Titoff. 

At  higher  temperatures  the  gases  do  not  obey  the 
law  expressed  by  the  formula  so  far  made  use  of.  This 


THE   PHENOMENA  OF   ADSORPTION.  65 

depends  upon  the  variation  in  the  heat  of  adsorption. 
Titoff  has  made  some  very  interesting  experiments 
regarding  this  quantity.  He  found  in  agreement  with 
some  old  experiments  of  Chappuis  that  the  first  traces 
of  gas  to  be  adsorbed  always  evolved  more  heat  than 
the  subsequent  additions,  as  will  be  clear  from  the 
following  figures,  observed  by  means  of  an  ice-calorim- 
eter, i.  e.y  at  0°. 

9o  Qo              q\  Q» 

Nitrogen 0.330  7392  0.21C  4700 

Carbonic  acid 0.347  7772  0.293  6564 

Ammonia 0.502  11245  0.384  9408 

(jo  is  the  number  of  calories  developed  by  one  cubic 
centimeter  of  gas  during  its  adsorption  in  a  large 
quantity  of  carbon;  #1  is  the  corresponding  heat  de- 
veloped, when  the  adsorption  has  already  proceeded  to 
a  certain  degree.  Qo  and  Qi  are  the  same  figures  for  one 
grammolecule,  corresponding  to  22,400  cubic  centi- 
meters. 
Now  the  second  law  of  thermodynamics  demands  that 

dlogp  _        Q 
dt      "  1.985  T2' 

Here  p  is  the  pressure  of  gas  which  is  in  equilibrium 
with  a  certain  adsorbed  quantity  a.  Therefore  if  Q 
were  constant  and  if  we  plotted  log  p  as  a  function  of 
log  a  at  different  temperatures  the  curves  so  obtained 
for  two  different  temperatures  should  be  equidistant 
from  one  another  for  all  values  of  p  or  a.  But  if  Q  is  not 
constant  but  greater  for  low  values  of  a,  as  is  actually 
the  case,  then  the  distance  between  the  two  curves 
ought  to  be  greater  at  lower  values  of  a  than  at  higher, 
as  is  really  found,  for  instance  with  carbonic  acid  ac- 
cording to  the  measurements  of  Titoff,  one  of  whose 


66 


THEORIES  OF  SOLUTIONS. 


diagrams  I  have  reproduced  here.  If  the  curves  were 
absolutely  equidistant  the  whole  way  and  our  equation 
were  valid  for  one  of  them,  for  instance  that  at  0°, 
then  it  would  hold  for  higher  temperatures,  with  only  a 
change  hi  the  constant  k.  Now  we  know  that  at  low 
values  of  a  the  distance  will  be  greater  than  at  higher 
values,  i.  e.,  p  must  be  too  great  and  as  k  is  proportional 


-W 


o 

FIG.  1. 


0.5 


1.0 


2.0 


to  p  (or  c,  cf.  the  formula  of  Schmidt)  k  also  must  be 
too  great.  This  is  the  real  reason  why  we  observe  an 
increase  of  k  with  diminishing  a  and  p  in  the  tables  given 
above.  At  higher  temperatures  this  disagreement  with 
our  formula  will  increase  more  and  more,  the  curves  will 
become  steeper  and  steeper.  The  slope  of  the  upper 
curves  towards  the  left  is  26°. 57,  corresponding  to  a  tan- 
gent =  0.5  and  for  them  a  is  nearly  proportional  to 
the  square  root  of  p  (at  low  values  of  a).  The  slope 


THE  PHENOMENA   OF  ADSORPTION.  67 

of  the  lowest  curve  on  its  left  side  is  nearly  45°,  corre- 
sponding to  a  tangent  =  1,  indicating  that  p  and  a 
are  proportional  to  each  other.  This  proportionality  is 
characteristic  for  gases  at  small  pressures  and  high 
temperatures;  for  hydrogen  according  to  Titoff  the  rule 
holds  even  at  the  lowest  temperature  examined  (—  79) 
and  the  highest  pressure  (72  cm.  Hg).  Therefore  in 
the  diagram  for  carbonic  acid — with  the  exception  of 
helium  and  hydrogen,  all  gases  examined  behave  in  the 
same  manner — the  curves  will  on  the  left  hand  have  a 
fan-like  distribution  with  an  angle  of  186.43.  At  suf- 
ficiently low  temperatures  even  helium  and  hydrogen 
would  without  doubt  obey  this  general  rule. 

It  may  be  remarked  here  that  in  some  cases  a  tangent 
exceeding  1  has  been  observed;  thus  for  helium  in  one 
case  (at  —  78°)  1.68,  and  for  methane  in  another  case 
(at  182°)  1.91  and  other  values  above  1  are  to  be  found 
in  nearly  all  series  of  observations,  but  probably  they 
are  due  to  accidental  errors  of  observation. 

Titoff  remarked  that  the  five  gases  observed  by  him 
showed  a  great  regularity,  indicating  that  the  quanti- 
ties of  different  gases  adsorbed  under  a  pressure  of  10 
cm.  Hg  run  parallel  to  the  values  of  a  in  van  der  Waals' 
equation,  which  indicate  the  attraction  of  the  mole- 
cules upon  one  another.  This  is  true  also  for  the  gases 
observed  by  Miss  Homfray  as  may  be  seen  from  the 
table  on  page  68. 

a  gives  the  constant  of  van  der  Waals,  A  the  quantity 
of  gas  adsorbed  on  one  g.  of  cocoanut-charcoal  at  a 
pressure  of  10  cm.  Hg  and  at  0°  C.  T  is  the  absolute 
critical  temperature  and  S  the  maximum  quantity  of 
gas  (in  cm.  of  0°  and  76  cm.  pressure)  which  can  be 


68  THEORIES  OF  SOLUTIONS. 

adsorbed  by  this  amount  of  charcoal.  It  should  be 
pointed  out  how  well  the  figures  of  Titoff  (marked  T.) 
agree  with  those  of  Miss  Homfray  (marked  H.);  as  a 
rule  the  charcoal  of  Miss  Homfray  seems  to  have  ad- 
sorbed about  10  per  cent,  less  than  that  of  Titoff. 

a                  A  T  S 

Ethylene 0.00883  41H.  284  58 

Ammonia 0.00808  71T.  403  158 

Carbonic  acid 0.00701  30T.    28H.  304  116 

Methane 0.00367  9.4H.  178  91 

Carbonic  oxide 0.00280  3.2H.  133  60 

Oxygen 0.00269  2.5H.  155  87 

Nitrogen 0.00268  ,      2.35T.  2.0H.        127  90 

Argon 0.00259  1.67H.  154  87 

Hydrogen 0.00042  0.227T.  32 

There  seems  to  be  an  exception  to  the  rule  given 
above,  in  that  A  is  less  for  ethylene  than  for  ammonia. 
This  depends  upon  the  fact  that  the  ethylene  was  very 
near  to  its  saturation  point  at  0°  C.  and  10  cm.  pressure. 
If  we  take  100°  C.  and  3.4  cm.  pressure  we  find  by 
interpolation  from  Titoff  s  figures  for  ammonia  A  = 
2.86  c.c.  whereas  Miss  Homfray  gives  for  ethylene  under 
similar  conditions  A  =  3.07.  The  exception  is  there- 
fore probably  not  genuine,  and  one  should  take  values  of 
A  for  adsorbed  quantities  far  below  the  limiting  values  S. 

The  parallelism  between  adsorption  and  the  constant 
a  suggested  the  idea  that  this  phenomenon  depends 
upon  the  attraction  of  the  molecules  of  the  adsorbed 
substance  and  the  carbon.  It  then  is  very  similar  to 
the  compression  of  a  liquid  under  high  pressure.  In  the 
one  case  through  increased  pressure  new  molecules  are 
carried  into  the  sphere  of  the  molecular  attraction  of 
the  carbon,  in  the  same  way  in  the  other  case,  new 
molecules  are  forced  into  the  sphere  of  molecular 


THE   PHENOMENA   OF  ADSORPTION.  69 

action.  Just  as  in  discussions  on  capillarity,  we  may 
regard  this  sphere  as  having  a  definite  radius;  if  it  has 
not,  but  if  the  attraction  decreases  continuously  out- 
wards, as  is  probably  the  case,  it  does  not  make  any 
great  difference,  for  we  have  then  only  to  consider  the 
space  around  a  molecule  in  which  the  molecular  action 
reaches  a  certain  value.  The  quantity  contained  in  this 
corresponds  to  the  adsorbed  quantity  a;  it  is  propor- 
tional to  the  density  of  the  fluid.  The  acting  pressure 
is  equal  to  the  sum  of  the  external  pressure  and  the 
term  a/02  in  van  der  Waals'  formula.  From  this  point 
of  view  I  have  calculated  the  figures  of  Amagat  on  the 
compressibility  of  liquids  and  I  quote  the  exceedingly 
regular  figures  for  ethyl  alcohol  at  0°. 
COMPRESSIBILITY  OF  ALCOHOL  AT  0°  ACCORDING  TO  AMAGAT,  S  =  1.2729. 

5,081  +3,000  atm.  1.1521  12,836 

4,937+2,500  "  1.1355  12,838 

4,775+2,000  "  1.1169  12,767 

4,592+1,500  "  1.0952  12,633 

4,385  +  1,000  "  1.0703  12,437 

4,140+    500  "  1.0399  12,126 

3,838+       1  "  1.0000  11,690 

The  agreement  is  excellent.  Here  k  decreases  with 
decreasing  pressure  in  contradistinction  to  the  case  with 
adsorption.  This  depends  upon  the  fact  that  the  heat  of 
evaporation  is  greater  for  the  compressed  fluid  than  for 
the  non-compressed,  and  the  difference  is  the  heat  of 
compression.  The  latter,  Q,  may  be  calculated  accord- 
ing to  the  following  formula,  deduced  from  the  second 
law  of  thermodynamics: 

Q  =  0.024  Tpa, 

where  T  is  the  absolute  temperature,  p  is  the  external 
pressure  in  atmospheres — I  have  taken  2000  in  my 


70  THEORIES  OF   SOLUTIONS. 

calculations — and  a  is  the  coefficient  of  cubical  ex- 
pansion from  0°  to  1°.  In  this  way  I  obtained  the 
following  table,  where  Q0  indicates  the  latent  heat  of 
evaporation  at  atmospheric  pressure,  feooo  and  ki  the 
values  of  the  constant  of  our  equation  at  2000  and  at 
1  atm.  pressure  respectively. 

B             Q  Qo  £±&  *,ooo  *,  •*£* 

Ethyl  ether 1.2642  21.2  93.5  1.227  6530  5078  1.284 

Ethyl  alcohol          1.2729  14.5  236.5  1.0613  12767  11690  1.092 

Sulphide  of  carbon  1.224  15.7  90.0  1.175  9755  8700  1.121 

With  increasing  temperature  Q0  generally  decreases, 
Q  on  the  contrary  increases,  since  a  as  well  as  T  does  so. 
Therefore  we  might  expect  that  the  constant  k  would 
increase  the  more  rapidly  with  pressure  the  higher  the 
temperature,  and  as  a  matter  of  fact,  this  rule  also  holds 
good,  the  ratio  K2ooo :  Ki  being  1.363  for  ether  at  50°, 
1.106  for  ethyl  alcohol  at  40°.4  and  1.144  for  sulphide 
of  carbon  at  49°.  15. 

Evidently  adsorption  is  a  manifestation  of  molecular 
attraction.  It  has  been  often  maintained  that  it  is 
due  to  surface  tension,  and  the  aggregation  of  the 
adsorbed  molecules  to  the  adsorbing  substance  was 
said  to  diminish  the  surface  tension.  On  the  other 
hand  Walden  has  shown  that  according  to  an  idea 
suggested  by  Stefan,  the  surface  tension  of  a  liquid 
is  proportional  to  the  surface  pressure,  which  again  is 
proportional  to  van  der  Waals'  constant  a  divided  by 
ft,  where  n  is  the  molecular  volume.  Hence  as  a  rule 
gases  ought  to  be  the  more  easily  adsorbed,  the  greater 
the  surface  tension  of  the  adsorbed  layer  against  the 
gas  would  be,  which  is  precisely  opposite  to  the  current 
ideas.  Lewis  also  has  shown  that  the  surface  tension 
theory  of  adsorption,  developed  by  Gibbs,  does  not 


THE   PHENOMENA  OF  ADSORPTION.  71 

agree  quantitatively  with  the  facts  of  experience.  It 
seems  therefore  as  if  surface  tension  did  not  play  the 
chief  r61e  in  adsorption  phenomena. 

I  wish  only  in  conclusion  to  call  attention  to  a  pe- 
culiarity which  has  been  observed  by  physiological 
chemists,  who  have  investigated  the  adsorption  of 
colloidal  substances.  They  have  found  that  in  most 
cases  the  adsorbed  quantity  is  nearly  independent  of  the 
concentration  of  the  colloid  in  the  surrounding  solution 
provided  that  the  same  quantity  of  adsorbing  powder 
was  used.  (Landsteiner  and  Uhlirz  for  the  adsorption 
of  euglobulin  on  kaolin:  Michaelis  and  Rona  for  the 
adsorption  of  albuminoses  or  peptones.)  This  regu- 
larity seems  at  first  to  indicate  that  a  kind  of  compound, 
in  constant  proportions,  is  formed  between  the  adsorb- 
ing powder  and  the  adsorbed  colloid.  But  it  is  very 
difficult  for  a  chemist  to  accept  such  a  solution.  Evi- 
dently the  right  explanation  is  that  as  a  rule  substances 
with  the  highest  critical  points,  i.  e.,  the  lowest  vapor 
pressures  possess  the  greatest  values  of  a,  as  an  inspec- 
tion of  the  tables  of  Landolt-Boernstein  will  show.  The 
colloids  investigated  possess  a  very  low  vapor  tension 
and  therefore  they  are  strongly  adsorbed,  so  that  the 
limiting  adsorption  is  nearly  reached  even  at  compara- 
tively low  concentrations,  and  therefore  adsorption  ap- 
parently occurs  in  nearly  constant  proportion  to  the 
amount  of  adsorbent  used.  Of  course,  the  limiting  value 
is  never  absolutely  reached,  but  within  the  errors  of  ob- 
servation it  may  already  be  reached  at  low  concentra- 
tions in  cases  such  as  those  mentioned.  This  instance 
is  certainly  not  devoid  of  interest,  for  it  shows  that  con- 
stant proportions  may  rule  in  aggregates  of  a  rather 
loose  nature. 


LECTURE  V. 

THE  ANALOGY  BETWEEN  THE  GASEOUS    AND  THE  DIS- 
SOLVED STATES  OF  MATTER. 

IT  is  well  known  to  all  of  us  that  the  present  great 
advance  in  physical  chemistry  is  due  chiefly  to  the 
introduction  of  two  theories,  the  one  expressing  the 
far-reaching  analogy  existing  between  the  gaseous  and 
the  dissolved  states  of  matter,  with  which  follows  the 
thermodynamic  treatment  of  chemical  equilibria  in 
solutions,  and  the  other  indicating  that  salts  (acids 
and  bases  are  regarded  as  hydrogen  salts  and  as 
hydrates  respectively)  are  in  solution  partially  dis- 
sociated into  their  ions.  As  a  rule  it  is  said  that  this 
new  development  came  abruptly  and  many  people 
believe  that  for  this  reason  the  merit  of  these  theories 
is  greatly  increased.  I  am  of  quite  an  opposite  opinion. 
The  ideas  mentioned  may  be  found  in  a  less  fully 
developed  state  in  older  speculations  regarding  the 
chemical  behavior  of  solutions  and  we  ought  to  lay 
great  stress  upon  this  fact,  for  it  is  the  most  convincing 
proof  of  their  soundness  that  they  should  have  de- 
veloped quite  continuously  and  organically  from  all 
the  results  of  chemical  experience.  Of  course  when 
they  at  first  took  form,  the  ideas  were  deduced  from  a 
rather  small  number  of  observations,  so  that  their  use- 
fulness was  not  very  evident  and  on  the  other  hand,  the 
conservative  majority  of  scientists  were  opposed  to  the 
introduction  of  new  notions  which  seemingly  compli- 

72 


ANALOGY  BETWEEN   STATES  OF  MATTEK.  73 

cated  their  conception  of  Nature.  The  new  points  of 
view  therefore  lived  a  latent  life,  being  again  and  again 
indicated,  until  there  had  been  collected  together  a 
quantity  of  experimental  material  sufficient  to  demand 
the  explanation  which  they  were  capable  of  giving. 
At  such  a  stage  in  the  evolution  of  new  ideas,  a  rapid 
propagation  of  them  takes  place  under  sharp  opposition 
from  the  teachers  of  the  old  conceptions  and  in  the  end 
they  receive  an  overwhelming  support  simply  because 
of  the  great  importance  of  the  phenomena  which  they 
alone  are  able  to  explain. 

This  normal  course  of  evolution  may  easily  be  traced 
for  the  modern  theory  of  physical  chemistry.  The  chief 
progress  in  it  is  due  to  the  discovery  that  the  molecules 
of  dissolved  substances  behave  in  a  manner  very  similar 
to  that  of  gases.  The  laws  governing  the  properties 
of  gases  are  well  known  and  simple;  by  their  application 
to  the  much  greater  and  more  important  group  of 
solutions  we  have  won  an  extremely  valuable  knowledge 
of  the  nature  of  solutions  which  play  by  far  the  fore- 
most role  in  chemistry.  At  the  same  time  the  far- 
reaching  use  of  the  laws  of  thermodynamics  in  this 
new  chapter  gave  it  its  strength  and  high  value.  In 
reality  the  first  application  of  thermodynamics  to  the 
phenomena  peculiar  to  solutions  is  independent  of  the 
introduction  of  the  laws  of  gases  in  this  chapter. 
Therefore,  in  the  first  instance,  we  have  to  treat  the 
growth  of  the  idea  of  the  analogy  between  gases  and 
dissolved  substances  as  the  chief  progress  and  there- 
after to  regard  the  increasing  application  of  the 
laws  of  thermodynamics  to  the  doctrine  of  solutions 
as  the  means  of  making  the  greatest  possible  use  of 


74  THEORIES  OF   SOLUTIONS. 

the  simultaneous  concepts  regarding  the  nature  of 
solutions. 

It  is  here  in  place  to  recall  the  interesting  statement 
of  Newton  that  the  dissolved  molecules  in  a  solution 
tend  to  get  away  from  each  other  so  that  they  finally 
become  distributed  uniformly  in  the  solvent. 

In  reality  this  idea  gives  a  neat  explanation  of  the 
phenomena  of  diffusion,  which  are  so  closely  related  to 
the  force  of  osmotic  pressure.  Newton  regarded  this 
tendency  of  dissolved  molecules  as  due  to  reciprocal 
repulsion  of  the  dissolved  molecules,  just  as  the  diffusion 
of  gas-molecules  may  be  regarded  as  effected  by  the 
mutual  repulsion  of  those  molecules.  One  might  well 
say  that  the  modern  views  regarding  the  analogy  be- 
tween gaseous  and  dissolved  substances  might  well  have 
been  developed  from  this  conception  of  Newton.  But 
the  time  was  then  not  ripe.  The  experimental  knowl- 
edge of  chemical  phenomena  was  too  scarce  for  the 
formulating  of  laws  regarding  them.  In  the  year  1839 
Gay-Lussac  expressed  opinions  which  possess  a  startling 
suggestion  of  modernity.  "As  the  effects  of  affinity 
do  not  change  with  temperature  (he  would  better  have 
said  change  but  slowly  with  temperature),  whereas 
dissolution  (solubility)  is  in  a  high  degree  dependent 
upon  it,  it  is  very  difficult  to  avoid  the  assumption  that 
in  dissolution  as  well  as  in  evaporation  the  product  is 
essentially  limited,  at  a  given  temperature,  by  the 
number  of  molecules  which  are  able  to  exist  in  a  certain 
volume  of  the  solvent  They  are  separated  from  this, 
just  as  gaseous  molecules  are  precipitated  by  a  lowering 

of  temperature Dissolution  is  therefore  hi  a 

high  degree  connected  with  evaporation,  namely  in  this 


ANALOGY  BETWEEN  STATES  OF  MATTER.  75 

respect  that  both  of  them  depend  on  the  temperature 
and  are  subject  to  its  variations.  Hence  they  ought  to 
show  if  not  a  complete  identity  in  their  effects  at  least 
a  great  analogy."  The  objection  that  in  some  cases, 
e.  g.,  with  sulphate  or  selenate  of  sodium,  the  solubility- 
curve  shows  a  break  and  sometimes  a  fall  with  increas- 
ing temperature,  whereas  this  is  not  the  case  with  the 
vapor-tension,  is  refuted  by  means  of  the  assertion 
that  at  the  temperature  where  the  break  occurs,  the 
substance  undergoing  solution  is  subject  to  a  transfor- 
mation. 

There  is,  however,  a  difference  between  a  gas  and  a 
dissolved  substance.  "The  molecules  of  the  gas  do  not 
need  a  solvent  to  hold  them  in  suspension  in  a  certain 
volume;  their  mutual  repulsion  is  enough  for  that 
purpose.  On  the  other  hand,  when  a  solid  or  liquid 
substance  is  dissolved,  its  molecules  would  not  remain 
in  the  limited  volume  if  they  were  not  united  by  their 
affinity  to  the  molecules  of  the  solvent." 

In  the  same  memoir  Gay-Lussac  criticises  the  theory 
of  Berthollet  according  to  which  the  precipitation  of, 
e.  g.,  sulphate  of  calcium  from  a  mixture  of  potassium 
sulphate  and  acetate  of  calcium  is  due  to  a  force  of 
cohesion  (measured  by  the  insolubility)  between  the 
molecules  of  the  sulphate  of  calcium,  which  acts  even 
before  the  substance  is  formed. 

Gay-Lussac  expressed  the  opinion  that  when  the  solu- 
tions of  two  salts  of  different  acids  and  bases  were 
mixed  all  the  four  possible  salts  were  formed,  e.  g.,  in 
the  example  above  there  existed  in  the  mixed  solution 
not  only  K2S04  and  Ca(CH3C02)2  but  also  KCH3C02 
and  CaS04.  If  then  one  of  these  four  is  very  slightly 


76  THEORIES   OF   SOLUTIONS. 

soluble,  so  that  the  solution  is  supersaturated  with 
regard  to  it,  it  is  precipitated,  and  thereupon  new 
molecules  of  CaS04  may  be  formed  in  the  liquid  and  a 
further  precipitate  occur.  In  the  same  way,  the  vola- 
tility of  one  of  the  products  may  exert  its  effect,  as 
Berthollet  contended.  Gay-Lussac  termed  "this  prin- 
ciple of  the  indifference  of  permutation"  between  the 
acids  and  bases  present  in  the  salts,  according  to  the 
chemical  doctrines  of  that  time,  equipollency,  and  the 
principle  has  found  its  simple  explanation  through  the 
electrolytic  dissociation  theory. 

Shortly  afterwards  a  Venetian  professor  Bartholomeo 
Bizio  expressed  similar  ideas  (1845).  He  came  back 
to  them  more  clearly  in  a  paper  of  1860,  printed  in  the 
memoirs  of  the  "Istituto  veneto."  Bellati  gives  (1895) 
an  analysis  of  Bizio's  work.  He  says  that  "  Bizio  re- 
garded the  dissolved  substance  as  an  elastic  vapor 
distributed  in  the  solvent.  The  difference  between  a 
dissolved  substance  and  a  gas  is  that  the  gas  does  not 
need  the  presence  of  the  molecules  of  the  solvent  and 
their  affinity  to  sustain  it  in  the  occupied  space."  This 
is  almost  word  for  word  the  statement  of  Gay-Lussac. 
The  different  colors  of  concentrated  and  diluted 
solutions  of  copper  chloride  were  explained  by  Bizio 
as  being  due  to  a  condensation  or  attenuation  of  the 
molecules,  i.  e.,  a  kind  of  dissociation.  Of  course  this 
idea  does  not  at  all  imply  a  dissociation  of  CuCl2  into 
its  ions  Cu  and  2C1,  as  Bellati  seems  inclined  to  suppose. 
"The  lack  of  precision  in  the  mechanical  conceptions 
of  Bizio  hindered  their  acceptance"  says  Bellati. 

Another  man  who  adhered  to  the  idea  of  a  close 
analogy  between  the  gaseous  and  the  dissolved  states 


ANALOGY  BETWEEN   STATES   OF  MATTER.  77 

was  Rosenstiehl,  who  expressed  his  views  in  a  note 
published  in  Paris  in  1870.  Rosenstiehl  says  that  he 
has  heard  that  Arago  has  been  the  first  to  compare  the 
phenomenon  of  solution  with  that  of  evaporation  but 
that  he  has  not  been  able  to  find  the  quotation  in 
which  this  view  is  expressed. — Probably  Arago  has  been 
confused  with  Gay-Lussac. — Rosenstiehl  drew  the  re- 
markable conclusion  that  "the  osmotic  force  is  analo- 
gous to  the  elastic  force  of  vapors.  Between  the  fluid 
column,  which  rises  in  an  osmometer  and  the  piston 
lifted  by  the  elastic  force  of  a  vapor  there  is  no  other 
difference  than  that  of  the  medium  in  which  the  work 
is  effected." 

In  1869  and  1873  Horstmann  deduced  from  thermo- 
dynamics the  laws  of  chemical  equilibrium  between 
gaseous  substances.  As  he  had  already  tested  his 
theoretical  results  on  known  equilibria  between  gases, 
he  next  subjected  an  equilibrium  between  dissolved 
substances,  namely  the  sulphates  and  carbonates  of 
potassium  and  of  barium  in  the  presence  of  precipitates 
of  the  two  barium  salts,  to  the  same  formula  as  that 
which  had  proved  valid  for  gases. 

This  equilibrium  had  been  studied  by  Guldberg  and 
Waage.  In  1864  they  had  elaborated  a  theory  of 
chemical  mass-action  according  to  which  the  "  chemical 
force  "  with  which  two  substances  A  and  B  in  concentra- 
tions CA  and  CB,  act  upon  each  other  is  proportional  to 
the  product  of  these  concentrations  raised  to  certain 
powers,  i.  e.,  to  C°A  .  C^.  If  then  two  new  substances 
E  and  F  were  formed,  as  for  instance  in  the  interaction 
of  two  salts,  and  equilibrium  was  reached  when  the  con- 
centrations of  those  substances  were  CE  and  Cp  then 


78  THEOEIES    OF   SOLUTIONS. 

the  chemical  forces  on  both  sides  must  be  of  the  same 
magnitude,  i.  e., 

K.CaA.Cb£  =  Ktf'z .  CfF. 

In  1867  they  simplified  this  formula  by  assuming 
a  =  &  =  e=/=l,  so  that  the  exponents  were  omitted. 
But  on  the  other  hand  they  introduced  a  complication 
by  supposing  that  the  chemical  forces  between  A  and 
B  were  not  only  dependent  on  their  own  concentrations 
but  also  on  the  concentrations  of  all  other  substances 
present  in  the  solution.  This  complication  was  intro- 
duced in  order  to  explain  the  influence  observed  in 
many  cases  of  foreign  substances  on  the  equilibrium. 

In  order  to  test  then-  ideas  Guldberg  and  Waage 
carried  out  a  great  number  of  experiments  both  on  the 
velocity  of  reaction  on  the  solution  of  metals  in  acids 
(in  which  case  the  velocity  was  taken  as  a  measure  of 
the  acting  chemical  force)  and  also  on  equilibria  in  which 
class  that  existing  between  K2C03  and  BaS04  on  the  one 
hand,  and  K2S04  and  BaC03  on  the  other  was  the 
principal  example. 

It  was  these  experiments  which  Horstmann  calcu- 
lated by  means  of  the  formula  which  had  proved  valid 
for  gases  and  he  found  them  to  be  in  good  agreement 
with  it.  He  concluded  that  the  "disgregation"  of  a 
(dissolved)  salt  depends  on  the  distance  between  its 
molecules,  in  the  same  manner  as  the  corresponding 
property  of  a  permanent  gas,  an  assumption  which  also 
from  other  considerations  seems  to  be  probable. 

In  1879  Guldberg  and  Waage  again  modified  their 
theory  and,  citing  Horstmann,  they  discarded  from  their 
equation  the  terms  referring  to  the  secondary  action  of 
foreign  substances.  In  this  way  the  analogy  between 


ANALOGY  BETWEEN   STATES  OF  MATTER.  79 

the  gases  and  the  dissolved  substances  in  their  chemical 
action  was  made  perfect.  They  say  that  "  these 
secondary  actions  may  be  neglected  if  the  solutions  are 
so  highly  diluted,  that  a  further  addition  of  solvent 
(water)  gives  rise  to  no  sensible  development  of  heat." 
Julius  Thomsen,  the  renowned  Danish  thermochemist, 
was  very  well  acquainted  with  the  work  of  Guldberg 
and  Waage  and  probably  he  was  influenced  by  it  when 
he  concluded  the  first  volume  of  his  "Thermochemische 
Untersuchungen"  (1882)  with  the  following  words: 
"The  aqueous  solutions  of  substances  contain  them  in 
a  condition  which,  just  as  the  gaseous  state,  reveals 
their  physical  qualities  in  the  simplest  manner,  so  that 
a  direct  comparison  of  the  two  states  is  permissible." 
At  that  tune  the  kinetic  theory  of  heat  was  widely 
accepted  by  physicists  and  chemists.  It  was  supported 
and  had  been  worked  out  by  such  authorities  as 
Clausius,  Maxwell  and  Boltzmann.  It  was,  in  fact, 
regarded  as  absolute  truth,  almost  like  the  two  laws  of 
thermodynamics.  This  whole  subject  was  therefore 
often  called  "  the  mechanical  theory  of  heat."  Later  on 
came  a  more  sceptical  time,  when  it  was  strongly  main- 
tained that  thermodynamics  may  exist  independently 
of  the  kinetic  theory  of  heat  and  when  it  was  regarded 
as  a  sign  of  progress  to  be  able  to  discard  all  mechanical 
views  regarding  the  nature  of  heat.  Nowadays  we 
have  come  back  to  the  old  view,  and  regard  it  as 
proved  that  the  molecules  possess  a  motion,  the  energy 
of  which  is  proportional  to  the  absolute  temperature 
(cf.  Lecture  II). 

Regarded  from  this  point  of  view  the  sublimation  of 
a  solid  substance  such  as  camphor  or  iodine  depends 


80  THEORIES   OF   SOLUTIONS. 

upon  the  fact  that  some  of  its  molecules  possess  such  a 
violent  motion  that  they  can  remove  themselves  from 
the  sphere  of  attraction  of  the  neighboring  molecules. 
In  the  same  manner  the  solution  of  a  solid  in  a  liquid 
must  be  explained  as  a  consequence  of  molecular 
motion  according  to  the  mechanical  theory  of  heat. 
This  idea  was  expressed  by  Tilden  and  Shenstone  (1883) 
"The  solution  of  a  solid  in  a  liquid  would  accordingly 
be  analogous  to  the  sublimation  of  such  a  solid  into  a 
gas  and  proceeds  from  the  intermixture  of  molecules 
detached  from  the  solid,  with  those  of  the  surrounding 
liquid.  Such  a  process  is  promoted  by  rise  of  tempera- 
ture, partly  because  the  molecules  of  the  still  solid 
substance  make  longer  excursions  from  their  normal 
centre,  partly  because  they  are  subjected  to  more 
violent  encounter  with  the  moving  molecules  of  liquid." 
.  .  .  "Such  a  theory  however,  serves  to  account  only 
for  the  initial  stage  in  the  process  of  solution,  and  does 
not  explain  the  selective  power  of  solvents  nor  the 
limitation  of  solvent  power  of  a  given  liquid." 

Walden  cites  Mendelejeff  as  a  precursor  of  the  sup- 
porters of  an  analogy  between  gases  and  dissolved 
substances.  Mendelejeff  had  stated  (1884)  that  the 
densities  of  aqueous  solutions  containing  1  molecule  of 
salts  to  every  100  molecules  of  water  generally  increase 
with  the  molecular  weight  of  the  salt.  (There  are  some 
exceptions  to  this  rule,  e.  g.,  solutions  of  Li-salts  are 
denser  than  equivalent  solutions  of  Nils-salts ;  compare 
' '  Valson's  moduli, ' '  Lecture  VI) .  "In  extremely  dilute 
solutions  the  dissolved  substance  exists  in  a  dispersed  or 
attenuated  state  similar  to  that  in  the  gaseous  state. 
Therefore  we  may  hope,  through  the  investigation  of 


ANALOGY  BETWEEN   STATES   OF   MATTER.  81 

the  densities  of  solutions  to  find  a  method  of  determining 
molecular  weights." 

On  closer  inspection  we  find  that  the  observed 
regularity  does  not  tell  us  much  more  than  that  salt- 
solutions  generally  possess  higher  densities,  the  more 
concentrated  they  are.  This  depends  upon  the  high 
specific  weight  of  salts  and  especially  of  those  with 
high  molecular  weights  compared  with  water.  If  we 
extend  the  comparison  to  solutions  of  substances  of  a 
lower  density  than  water,  such  as  alcohol,  the  cause 
of  the  regularity  is  evident.  We  must  therefore  reject 
the  claims  raised  in  favor  of  Mendelejeff  in  this  depart- 
ment. 

As  is  seen  from  the  quotations  above,  the  great 
analogy  between  gases  and  dissolved  substances  was 
admitted  by  a  great  number  of  leading  chemists.  In 
order  to  give  the  required  force  to  these  opinions  it  was 
necessary  to  apply  the  laws  of  thermodynamics  to 
them  and  this  was  done  by  van't  Hoff.  To  understand 
the  development  of  this  side  of  chemical  science  we  shall 
give  a  short  review  of  the  earliest  work  in  this  line. 

As  early  as  1858  Kirchhoff  had  published  some 
theoretical  thermo-dynamical  considerations  on  the  va- 
por pressures  of  solutions,  especially  of  sulphuric  acid. 
In  1867,  1868  and  especially  in  1870,  Guldberg  worked 
out  this  important  section  of  science  in  a  most  remark- 
able manner.  He  demonstrated  that  the  lowering  of 
the  freezing  point  of  a  solution  under  that  of  the  solvent 
as  well  as  the  corresponding  increase  of  its  boiling  point 
is  proportional  to  the  corresponding  lowering  of  its 
vapor  tension  and  gave  the  constants  which  represent 
the  factors  of  proportionality.  He  verified  his  theo- 


82  THEORIES   OF   SOLUTIONS. 

retical  deductions  by  means  of  the  figures  of  Wullner  and 
of  Riidorff  concerning  the  behavior  of  salt  solutions  in 
water.  We  now  know  quite  well  how  important  the 
similar  deductions  were  later  on  in  the  hands  of  van't 
Hoff.  Raoult  (1878  and  1882)  deduced  these  laws 
experimentally  a  little  while  afterwards  and  found  the 
true  law  of  depression  of  the  vapor-pressure: 

-1          n 


where  p  and  pi  are  the  vapor-pressures  of  pure  solvent 
and  of  the  solution  in  which  n  molecules  of  dissolved 
substance  are  mixed  with  N  molecules  of  solvent. 
Guldberg  also  in  1870  deduced  the  law  of  change  of 
solubility  with  temperature  and  pressure  later  deduced 
by  van't  Hoff.  He  even  showed  how  the  relative  de- 
pression of  the  vapor-pressure  changes  with  temperature. 
Another  great  advance  was  made  in  1869  in  Horst- 
mann's  application  of  Carnot's  theorem  (or  its  special 
form,  the  formula  of  Clapeyron)  to  the  evaporation  and 
simultaneous  dissociation  of  sal-ammonia,  and  he  cal- 
culated its  heat  of  evaporation  from  the  observed  vapor- 
pressure  and  found  it  to  correspond  very  well  with  that 
experimentally  determined  by  Marignac.  The  calcula- 
tion was  exactly  similar  to  that  by  which  the  heat  of 
evaporation  of  water  is  found  from  its  vapor-pressure  at 
different  temperatures.  A  similar  calculation  was  made 
by  him  in  1870  for  the  evolution  of  carbonic  acid  from 
carbonate  of  calcium  according  to  Debray's  experiments 
and  for  the  dissociation  of  Na^HPC^  +  12H20  into 
NasHP04  +  7H2O  and  water  vapor.  In  1872  Guldberg 
made  similar  calculations  for  the  dissociation  pressure 


ANALOGY  BETWEEN  STATES  OF  MATTER.          83 

of  calcium  carbonate  and  deduced  the  famous  formula: 


where  p  is  the  dissociation  pressure,  T  the  absolute 
temperature,  R  the  gas  constant,  A  the  inverse  value 
(1/426)  of  the  mechanical  equivalent  of  heat,  and  q  the 
heat  of  dissociation  of  1  gram.  This  formula  is  sim- 
plified to  the  second  form  if  Q  is  the  heat  of  dissociation 
of  1  grammolecule,  since  then  AR  =  2  (better  1.985), 
as  Guldberg  had  shown  in  1870.' 

In  1873  Horstmann  wrote  his  famous  "Theorie  der 
Dissociation"  where  he  treats  the  general  problem  of 
dissociation  of  gaseous  substances,  and  applies  the 
results  to  the  investigations  of  Wiirtz  on  amylene 
hydrobromide  C6HnBr  and  to  those  of  Wiirtz  and 
Cahours  on  pentachloride  of  phosphorus  (PC15). 
Here  he  finds  the  great  analogy  between  dilute  solu- 
tions and  gases.  He  quotes  the  figures  of  Thomsen 
regarding  the  " avidity"  of  sulphuric  and  nitric  acid 
towards  sodium  hydrate  and  those  of  Guldberg  and 
Waage  on  the  reaction  between  barium  sulphate  and 
potassium  carbonate  at  100°  which  had  served  the 
latter  when  testing  then*  law  of  mass  action,  a  law  which 
is  also  valid  for  the  reactions  of  gases.  In  this  way 
Horstmann  was  led  to  the  conclusion  regarding  the 
analogy  between  dilute  solutions  and  gases,  cited 
above. 

In  1878  appeared  the  far-reaching  investigations  of 
Willard  Gibbs  on  the  application  of  thermo-dynamics 
to  chemical  equilibria.  In  this  work  all  conceivable 
problems  in  this  field  of  science  are  treated  theoretically. 


84  THEORIES  OF  SOLUTIONS. 

But  his  important  deductions  were  concealed  in  academ- 
ical transactions,  which  were  only  very  little  known 
and  therefore  did  not  exert  any  sensible  influence  on 
scientific  development.  In  1882  Helmholtz  independ- 
ently wrote  his  well-known  memoir  on  "free  energy ," 
containing  general  deductions  very  similar  to  those  of 
Gibbs.  In  1885  Le  Chatelier  published  his  interesting 
memoir,  in  which  he,  basing  his  theory  on  Wiillner's 
experiments,  shows  that  the  equation  of  Clapeyron  may 
be  used  for  calculating  the  change  of  the  solubility  of 
a  substance  with  temperature. 

The  ground  was  therefore  very  well  prepared  from 
the  theoretical  side.  But  the  last  simple  grasp  of  the 
problem  failed,  until  van't  Hoff  in  1885  demonstrated 
the  widely  extended  analogy  between  substances  at 
high  dilution  and  gases  in  their  physical  and  chemical 
behavior.  A  year  before  this,  he  had  published  his 
important  "Etudes  de  dynamique  chimique,"  where  he 
gave  the  formula  found  before  byGuldbergfor  the  change 
of  the  pressure  of  dissociation  with  temperature  and 
showed  that  it  also  holds  good  for  the  change  of  the 
constant  of  a  chemical  equilibrium  with  temperature, 
if  this  constant  replaces  p  and  if  Q  represents  the  heat 
evolved  in  the  reaction  considered.  A  similar  expression 
was  used  by  Boltzmann  in  the  same  year  for  calculating 
the  heats  of  dissociation  of  iodine  and  of  N204.  And 
also  in  the  same  year  Le  Chatelier  had  a  little  earlier 
than  van't  Hoff  found  the  same  general  qualitative  ex- 
pression for  the  change  of  chemical  equilibrium  with 
temperature  as  is  contained  in  van't  HofFs  quantitative 
formula. 

Van't   HcfTs   fundamental  discovery  in   1885   was 


ANALOGY  BETWEEN   STATES   OF   MATTER.  85 

directly  due  to  the  investigations  of  De  Vries  and 
Pfeffer  on  the  osmotic  pressure  of  certain  plant  cells. 
They  investigated  a  property  well-known  to  cell-phys- 
iologists, namely  that  if  cells  are  placed  in  aqueous 
solutions  they  take  water  from  the  solution,  if  this 
is  weak,  and  give  up  water  to  it,  if  it  is  strong.  With 
a  certain  concentration  of  the  solution  equilibrium  is 
obtained.  De  Vries  found  that  solutions  of  glycerol 
or  of  cane  sugar,  which  contain  the  same  number  of 
molecules  per  liter,  are  in  equilibrium  with  the  same  cells. 
Also  equimolecular  solutions  of  KC1,  NaCl,  KN03  and 
NaN03  are  found  to  be  in  equilibrium  with  the  same 
cells.  But  these  salt  solutions  are  only  0.6  times  as 
concentrated  as  the  corresponding  solutions  of  glycerol 
or  cane  sugar  which  are  in  equilibrium  with  the  same 
cells. 

Now  Moritz  Traube  in  1867  had  given  a  method  of 
preparing  artificial  cells,  which  possess  the  properties 
of  attracting  water  from  or  of  giving  it  up  to  surrround- 
ing  aqueous  solutions  according  to  their  concentrations, 
just  like  natural  cells.  In  1877  Pfeffer  used  Traube's 
cells  for  measuring  the  force  with  which  distilled  water 
was  attracted  into  such  a  cell  filled  with  a  solution  of, 
e.  g.y  1  per  cent,  cane  sugar.  If  the  solution  in  the  cell 
is  subjected  to  a  certain  pressure  the  water  is  driven  out 
from  the  sugar  solution :  the  sugar  itself  does  not  pass 
through  the  cell  walls,  which  latter  consisted  of  a  thin 
membrane  of  ferro-cyanide  of  copper,  precipitated  in  the 
porous  walls  of  an  earthenware  vessel.  At  a  certain 
pressure,  which  was  found  to  be  505  millimeters  of 
mercury  at  6.8°  C.,  equilibrium  was  reached  so  that 
no  water  went  into  the  cell  from  the  surrounding  dis- 


86  THEORIES  OF  SOLUTIONS. 

tilled  water  and  no  water  was  pressed  out  from  the  solu- 
tion of  cane  sugar  through  the  cell  walls.  This  pressure, 
the  so-called  osmotic  pressure  of  a  solution  of  1  per  cent, 
cane-sugar,  increases  with  temperature.  It  is  nearly 
proportional  to  the  concentration  of  the  sugar-solu- 
tion when  this  is  changed. 

These  results  of  Pfeffer's  measurements  were  com- 
municated to  van't  Hoff  by  his  friend  De  Vries,  who 
asked  for  a  theoretical  explanation.  Van't  Hoff  made 
the  following  simple  calculation.  A  gas  containing 
one  gram  molecule  in  22,400  c.c.  at  0°  C.  possesses  a 
pressure  of  just  1  atmosphere  or  760  millimeters  of  mer- 
cury. At  6.8°  C.  the  pressure  is  a  little  higher,  namely 
779  millimeters,  according  to  the  law  of  Gay-Lussac.  If 
this  gas  was  expanded  until  it  contained  one  molecule  in 
34,200  c.c.,  which  is  the  concentration  of  a  1  per  cent,  so- 
lution of  cane  sugar — the  molecular  weight  of  cane  sugar 
being  342 — its  pressure  at  6.8°  C.  would  according  to 
Boyle's  law  be  508  millimeters.  This  figure  agrees 
within  1  per  cent,  and  within  the  errors  of  observation  in 
Pfeffer's  experiments  with  that,  505  mm.,  found  for 
the  osmotic  pressure  of  an  equi-molecular  solution  of  cane 
sugar.  In  other  words  the  osmotic  pressure  of  this 
solution  is  equal  to  the  pressure  of  a  gas  containing  the 
same  number  of  molecules  in  the  same  volume.  Since 
further  the  osmotic  pressure  increases  proportionally 
to  the  concentration  (just  as  the  gas  pressure  does 
according  to  Boyle's  law)  and  within  the  errors  of 
experiment  as  van't  Hoff  deduced  from  Pfeffer's  fig- 
ures, also  to  the  absolute  temperature  (as  in  Gay- 
Lussac's  law  for  gases),  there  exists  a  perfect  analogy 
between  the  osmotic  pressure  of  a  solution  (of  cane  sugar) 


ANALOGY  BETWEEN   STATES   OF  MATTER.  87 

and  the  pressure  of  a  gas  containing  the  same  number 
of  molecules  in  the  same  volume. 

As  soon  as  this  fundamental  fact  was  stated,  van't 
Hoff  applied  all  the  laws  which  had  been  deduced 
from  thermodynamics  for  the  pressures  of  gases  and 
for  saturated  vapors,  which  correspond  to  saturated 
solutions,  to  the  osmotic  pressures  of  dissolved  sub- 
stances. Thus  he  found  that  he  was  able  to  deduce 
the  general  law  of  chemical  equilibria  (Guldberg  and 
Waage's  law);  the  law  of  the  influence  of  pressure  on 
chemical  equilibria  (Le  Chatelier's  law);  the  law  of 
the  temperature-variation  of  chemical  equilibria;  the 
law  of  partition  of  a  substance  between  two  different 
phases  (law  of  Henry  and  law  of  Berthelot  and  Jung- 
fleisch);  the  laws  of  vapor  pressure  and  freezing  point 
of  solutions  (laws  of  Raoult;  the  third  law  of  Raoult 
regarding  the  boiling  points  was  a  little  later  deduced 
by  Arrhenius,  the  connection  between  these  laws  having 
already  been  pointed  out  by  Guldberg);  the  law  of 
isotonic  solutions  (law  of  De  Vries) ;  the  law  governing 
the  partition  of  a  base  between  two  acids  according  to 
the  experiments  of  Jellet,  Julius  Thomsen  and  Ostwald; 
the  law  of  the  change  of  solubility  with  temperature, 
partially  deduced  before  by  Guldberg;  the  regularities 
found  in  the  action  of  water  on  salts,  according  to  ex- 
periments of  Ditte;  and  the  law  with  regard  to  the 
electromotive  force  of  galvanic  cells,  concerning  which 
Gibbs  and  Helmholtz  had  some  years  before  (1878  and 
1882)  written  fundamental  works,  in  which  they  intro- 
duced the  conception  of  "free  energy." 

The  whole  investigation  of  van't  Hoff  (1885)  was 


88  THEORIES  OF   SOLUTIONS. 

a  triumphal  march  through  the  different  domains  of 
physical  chemistry;  only  one  difficulty,  but  a  rather 
severe  one,  was  found.  The  great  majority  of  sub- 
stances examined  did  not  follow  the  law  of  Avogadro, 
as  cane  sugar  did.  This  was  already  manifest  from  De 
Vries'  investigations,  according  to  which  one  molecule 
of  sodium  chloride  exerts  the  same  osmotic  pressure  as 
about  1.7  molecules  of  cane-sugar  dissolved  in  the  same 
quantity  of  water.  To  account  for  this  difference, 
van't  Hoff  introduced  a  coefficient  i  (the  isotonic  co- 
efficient) which  was  determined  experimentally.  This 
coefficient  entered  as  an  exponent  into  the  formula  for 
the  chemical  equilibrium,  so  that  Guldberg  and  Waage's 
law  was  reduced  to  its  first  form  (of  1864). 

This  was  a  great  inconvenience,  for  it  really  spoilt 
the  analogy  between  the  dilute  and  the  gaseous  states  of 
matter,  but  it  was  very  soon  eliminated  by  the  theory 
of  electrolytic  dissociation.  Therefore  in  the  second 
edition  (1887)  of  his  fundamental  memoir  van't  Hoff 
added  the  following  remarkable  words  regarding  the 
necessity  of  introducing  the  coefficient!:  " Thus  it 
seems  rather  adventurous  to  put  Avogadro's  law  so 
strongly  in  the  foreground,  as  I  have  done  in  this  memoir " 
(in  the  memoir  of  1885  very  much  less  stress  was  laid 
on  the  validity  of  Avogadro's  law  for  solutions)  "and 
I  would  not  have  decided  to  do  so,  if  Arrhenius  had 
not,  in  a  letter,  pointed  out  the  probability,  that  with 
salts  and  similar  substances  the  question  is  really  one 
of  their  division  into  ions." 

A  theoretical  deduction  of  the  law  of  van't  Hoff 
regarding  the  analogy  of  the  dilute  and  the  gaseous 


ANALOGY   BETWEEN   STATES   OF  MATTER.  89 

state  of  matter  was  given  by  Planck  (1887)  in  order 
to  explain  the  anomalies  which  led  van't  Hoff  to  intro- 
duce the  coefficient  i.  He  started  from  the  hypothesis 
that  for  the  energy  U  of  a  dilute  solution  containing  n 
molecules  of  solvent  and  HI,  n2,  n3,  etc.,  molecules  of 
dissolved  substances  the  following  expression  is  valid 
(at  constant  temperature): 


where  u,  Ui,  u%,  uz,  etc.,  may  be  regarded  as  the  partial 
energies  of  one  molecule  of  solvent  or  of  dissolved 
substances,  respectively,  in  very  dilute  solutions  —  so 
dilute  that  on  further  addition  of  solvent  no  heat  is 
evolved.  The  same  expression  is  valid  for  a  mixture 
of  gases  in  the  same  proportions.  Therefore  the  gas- 
laws  hold  good  for  dissolved  substances.  The  abnormal 
behavior  of  salts  is  due  to  a  dissociation  of  their 
molecules. 

The  weakness  of  this  deduction  is  evident;  it  might 
be  that  the  expression  quoted  was  true  only  for  solu- 
tions so  extremely  dilute  that  they  were  not  capable 
of  being  measured.  Planck  also  conceded  (1892)  that 
by  means  of  thermodynamics  "nothing  could  be 
demonstrated  regarding  the  qualities  of  the  dissolved 
molecules,  either  in  respect  to  their  chemical  or  electrical 
properties,  and  that  to  this  method  could  be  ascribed 
no  convincing  conclusion,  but  only  a  heuristic  significa- 
tion." 

Certainly  the  adherence  of  Planck  and  at  the  same 
time  of  Boltzmann,  the  two  most  prominent  representa- 
tives of  mathematical  physics  in  Germany,  helped  in  a 


90  THEORIES  OF  SOLUTIONS. 

high  degree  to  protect  the  new  theory  from  the  attacks 
of  physicists.  By  their  great  authority  they  also  gave 
a  strong  support  to  the  new  ideas  in  the  eyes  of  chemists 
and  of  scientists  hi  general,  and  this  was  of  a  value 
which  should  not  be  underestimated,  especially  during 
the  first  years  of  the  growth  and  propagation  of  these 
ideas,  which  otherwise  seemed  revolutionary  and  there- 
fore evoked  a  rather  determined  resistance. 


LECTURE  VI. 

DEVELOPMENT  OF   THE   THEORY   OF  ELECTROLYTIC 
DISSOCIATION. 

THERE  have  been  two  different  roads,  which  have 
led  to  views  related  to  the  modern  theory  of  electrolytic 
dissociation,  one  empirical  and  one  theoretical.  The 
empirical  one,  inaugurated  by  Valson,  is  founded  on 
the  so-called  additive  properties  of  salt-solutions,  the 
theoretical  one,  first  entered  upon  by  Gay-Lussac, 
Williamson  and  Clausius,  is  based  upon  considerations 
of  the  progress  of  chemical  processes  or  the  passage  of 
electricity  through  salt  solutions.  Under  salts  are  here 
included  even  acids  and  bases. 

Valson  measured  the  height  to  which  salt-solutions 
rise  in  capillary  tubes  of  glass.  These  heights  are  pro- 
portional to  the  capillary  constant  and  inversely  pro- 
portional to  the  density  of  the  solution  (provided  of 
course  that  the  internal  diameter  of  the  capillary  tube 
remains  the  same).  When  he  compared  normal  solu- 
tions, which  contain  equivalent  weights  of  different 
salts  in  one  liter  of  the  solution,  he  stated  that  the 
capillary  height  might  be  conveniently  calculated  as 
the  sum  of  three  components,  the  one  the  capillary 
height  of  pure  water  and  the  other  two  corrections, 
which  should  be  added,  the  one  for  the  positive  radical 
(now  we  say  ion)  of  the  salt  and  the  other  for  its  nega- 
tive radical.  These  two  corrections,  which  are  gen- 
erally negative,  always  remain  the  same  for  the  same 

91 


92  THEORIES  OF   SOLUTIONS. 

radical  independent  of  the  other  radical  to  which  it  is 
bound  in  the  investigated  salt.  This  is  most  clearly 
demonstrated  in  the  so-called  additive  scheme,  which 
shows  that  the  difference  of  the  investigated  property 
(here  capillary  height)  between  a  chloride  and  a  nitrate 
is  the  same  for  the  potassium  salts  as  for  the  sodium 
or  lithium  or  calcium  salts,  if  the  solutions  possess  the 
same  number  of  equivalents  per  liter.  The  same  is 
true  of  the  difference  between  chlorides  and  sulphates, 
chlorides  and  carbonates  and  so  forth.  As  an  example 
we  give  the  following  differences  in  millimeters  of  the 
capillary  heights  for  normal  solutions.  (The  diameter 
of  the  glass  tube  was  0.5  mm.,  the  temperature  +  15° 
C.): 

NH4C1  60.9,  KC1  59.3,  Y2  CdCl2  56.5,  LiCl  60.8,  Y2  SrClj  58.0,  Yz  BaCl2 

56.9,  Yz  ZnCl2  58.1,  NaCl  59.6,  H2O  60.6. 
Cl-Br:  NH4  2.2,  K  2.2,  Y2  Cd  2.0,  Mean  2.1. 
Cl-I:  Li  3.8,  K  3.9,  Yz  Ba  3.8,  Yz  Zn  4.1,  Yz  Cd  4.0,  Mean  3.9 
Cl-SO4/2:  NH4 1.2,  K  1.1,  Na  1.2,  Yz  Zn  1.1,  Yz  Cd  1.2,  Mean  1.2. 
C1-NO3:  NH4 1.1,  K  0.9,  Yz  Sr  1.1,  Yz  Ba  1.0,  Mean  1.0. 

The  capillary  height  of  water  was  60.6  mm.,  and  was 
only  exceeded  by  the  capillary  heights  of  normal  solu- 
tions of  NH4C1  and  LiCl,  amongst  the  solutions  exam- 
ined. At  the  head  are  written  the  capillary  heights  of 
the  chlorides  from  which  the  corresponding  values  of 
the  other  solutions  may  be  calculated.  The  third  line 
regarding  Cl-Br  indicates  that  the  capillary  height  of  a 
normal  solution  of  NH4Br  is  60.9-2.2  =  58.7,  of  KBr 
59.3  -  2.2  =  57.1  and  of  ^CdBr2  56.5  -  2.0  =  54.5. 

The  additive  scheme  demands  that  all  the  figures 
for  Cl-Br  should  be  equal  and  so  forth.  In  reality  this 
was  found  by  Valson  to  correspond  very  nearly  to  his 
measurements. 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.  93 

Valson  has  drawn  some  conclusions  from  his  measure- 
ments which  I  cite  verbally  because  they  have  some- 
times been  misunderstood,  which  can  well  happen,  as 
many  technical  terms  were  used  in  a  different  sense 
than  now.  He  says:  " Experience  shows  that  the 
effects  of  capillarity  are  nearly  proportional  to  the 
quantity  (concentration)  of  the  examined  substance, 
but  this  is  not  true  for  concentrated  solutions,  in  which 
the  actions  of  the  molecules  are  not  independent  of 
each  other.  It  therefore  seems  that  it  is  necessary  that 
the  saline  molecules  occur  in  a  medium  of  sufficient 
volume,  in  order  that  they  may  be  regarded  as  having 
reached  the  state  of  liberty.  It  is  something  analogous 
to  the  circumstances  of  the  dissociation  phenomena  as 
stated  by  Mr.  Henri  Sainte-Claire-Deville,  according 
to  which  the  molecules  of  different  substances  do  not 
manifest  their  specific  properties  and  do  not  give  their 
characteristic  effects,  if  they  are  not  brought  to  a 
suitable  degree  of  attenuation  (desagr£gation)." 

Here  there  is  no  question  of  a  dissociation  of  the 
salt  molecules,  into  their  ions,  or  even  of  the  additive 
properties,  but  only  of  the  regularity  that  the  difference 
of  the  capillary  height  of  water  and  that  of  a  dilute  salt 
solution  is  proportional  to  its  concentration,  from  which 
Valson  concludes  that  the  molecules  are  in  an  ideal 
state  showing  many  regularities  when  they  are  diluted 
with  a  great  quantity  of  water.  This  ideal  state 
vanishes  with  higher  concentrations,  for  which  the  said 
regularity  is  not  observed.  This  opinion  of  Valson  is 
still  more  emphasized  in  the  following  words:  "If  one 
combines  the  metals  with  different  metalloidic  radicles 
as  for  instance  oxygen,  chlorine,  bromine,  iodine,  etc., 


94  THEORIES  OF  SOLUTIONS. 

one  finds  that  the  caloric  equivalents  of  the  binary 
compounds,  referred  to  the  dissolved  state,  exhibit  con- 
stant differences  amongst  each  other.  One  may  explain 
this  analogy  in  remarking  that  the  capillary  phenomena 
as  well  as  the  calorific  ones,  depend  finally  on  the  same 
property  of  the  molecular  movement,  which  generally 
is  called  vis  viva."  This  conclusion  is  rather  confusing, 
the  capillary  phenomena  really  depend  upon  surface 
tension  and  are  diminished  when  the  molecular  move- 
ment (vis  viva)  increases  with  temperature. 

In  reality  the  circumstance,  that  the  additive  scheme 
holds  to  a  certain  but  rather  low  degree  even  for  the 
heats  of  combination,  reduced  to  the  dissolved  state,  has 
been  taken  as  an  argument  against  the  dissociation 
theory,  and  therefore  we  shall  come  back  to  this  special 
case  later  on. 

The  capillary  height  is  proportional  to  the  capillary 
constant,  which  shows  very  small  inequality  for  different 
normal  solutions,  and  inversely  proportional  to  the 
specific  weight  of  the  solution,  which  latter  is  subject 
to  a  rather  great  variation.  Therefore  the  values  of 
the  capillary  height  show  nearly  the  same  regularities 
as  the  specific  weights  of  normal  solutions,  or  better, 
as  the  inverse  value  of  this  property,  which  is  generally 
called  the  specific  volume.  It  was  therefore  an  advance 
when  Valson  a  little  later  examined  the  specific  weights 
of  normal  solutions  and  there  found  regularities  similar 
to  those  for  the  capillary  height.  Later  on  Favre  and 
Valson  examined  the  changes  of  volume  which  occur 
on  the  solution  of  salts  in  water.  On  absolutely  inad- 
missible grounds  they  calculated  the  heat  which  occurs 
on  compressing  one  liter  of  water  to  999  c.c.  at  15°  C., 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.  95 

to  be  7,576  cal.,  whereas  in  reality  it  is  only  22.3  cal. 
(cf .  p.  69  above) .  On  the  solution  of  one  gram  equivalent 
of  a  salt  in  water  sometimes  a  contraction  of  20  c.c.  is 
observed,  which  on  their  supposition  corresponded  to 
about  150,000  cal.,  and  arguing  from  this,  they  stated 
that  an  enormous  change  of  the  salt  had  taken  place, 
which  manifested  itself  as  a  "reciprocal  independency" 
of  the  radicals  of  the  salt  "which  it  would  be  difficult 
to  define  now  but  which  is  very  different  from  then* 
original  state."  "The  solution  has  the  effect  that  it 
gives  the  elements  of  the  dissolved  substances  an 
independency  of  each  other."  It  may  be  remarked 
here  that  the  solution  of  non-electrolytes,  e.  g.,  of 
alcohol,  in  water,  gives  rise  to  similar  great  changes  of 
volume. 

Evidently  this  whole  calculation  and  its  consequences 
are  absolutely  erroneous.  This  becomes  quite  clear 
when  we  say  that  Favre  and  Valson  would  have  found 
an  infinite  value  for  the  calculated  evolution  of  heat, 
if  they  had  chosen  the  temperature  at  which  water 
has  its  maximal  density,  and  this  value  would  have 
been  +  oo  above  and  —  oo  below  this  temperature. 
The  authors  demonstrated  by  experiments  that  the 
different  kinds  of  alums  are  to  a  great  extent  decom- 
posed upon  dilution  into  the  two  component  sulphates, 
but  that  is  something  wholly  different  from  the  now 
pretended  decomposition  of,  e.  0.,  NaCl  intoNa  and  Cl. 
We  must  therefore  say  that  the  ideas  which  have  been 
developed  by  Favre  and  Valson  are  rather  far  remote 
from  the  theory  of  electrolytic  dissociation. 

On  a  closer  investigation  of  the  properties  of  salt 
solutions  their  additive  character  was  shown  in  many 


96  THEORIES  OF   SOLUTIONS. 

cases.  Thus  Kohlrausch  found  that  the  conductivity 
of  a  salt  solution  might  be  expressed  as  the  sum  of  two 
conductivities,  the  one  valid  for  the  anion,  the  other  for 
the  cation  of  the  salt.  This  rule  of  the  "  independent 
movement  of  the  ions"  held  only  within  the  same  group 
of  salts,  e.g.j  the  salts  composed  of  two  monovalent  ions 
such  as  KC1.  Other  values  of  the  conductivity  of  the 
different  ions  were  obtained  for  salts  consisting  of  one 
bivalent  and  two  monovalent  ions  such  as  K2S04  orBaC!2 
and  still  others  for  salts  composed  of  two  bivalent  ions 
such  as  MgS04.  Gladstone  and  Bender  observed  simi- 
lar regularities  for  the  refractive  index  of  solutions, 
Jahn  for  the  magnetic  rotation  of  the  plane  of  polariza- 
tion, G.  Wiedemann  for  the  molecular  magnetism, 
Oudemans  and  Landolt  for  the  natural  rotatory  power  of 
the  plane  of  polarization.  The  most  evident  example 
was  the  thermoneutrality  of  salts  stated  by  Hess  as 
early  as  1840. 

The  most  accurate  measurements  concerning  the 
additive  properties  of  salt  solutions  and  just  those 
properties  which  were  at  first  considered  by  Valson,  are 
due  to  Rontgen  and  Schneider. 

For  the  relative  compressibilities  of  0.7  normal  salt 
solutions  (that  of  water  =  1,000)  they  found  the 
following  values 


I 

H 

Diff. 

NH4 

954 

Diff. 

14 

Li 

940 

Diff. 

8 

K 
932 

Diff. 
8 

Na 

924 

N03 

981 

27 

954 

20 

934 

4 

930 

8 

922 

Br 

981 

28 

953 

19 

934 

4 

930 

7 

923 

Cl 

974 

29 

945 

17 

928 

9 

919 

2 

917 

OH 

1,000 

(8) 

992 

(97) 

895 

11 

884 

3 

881 

2^04 

970 

(117) 

853 

(40) 

813 

9 

804 

1 

803 

jCOs 



— 



— 



- 

798 

1 

797 

Mean  28  17 


THEORY  OF  ELECTROLYTIC   DISSOCIATION.  97 

The  relative  molecular  volumes  of  1.5  normal  solu- 
tions were: 

NH4       Diff.         K          Diff.       H         Diff.       Li          Diff.      Na 


I 

1,048 

7 

1,041 

— 



- 

1,025 

2 

1,023 

N03 

1,043 

11 

1,032 

14 

1,018 

2 

1,016 

-1 

1,017 

Br 

1,038 

13 

1,025 

14 

1,011 

0 

1,011 

1 

1,010 

Cl 

1,028 

12 

1,016 

14 

1,002 

1 

1,001 

0 

1,001 

OH 

1,036 

(52) 

984 

(-16) 

1,000 

(30) 

970 

0 

970 

2bO4 

1,066 

— 



— 

1,027 

(20) 

1,007 

— 

— 

2C03 

— 

— 

1,012 

— 



— 



— 

984 

Mean  10  14  1  1 

By  molecular  volume  of  the  solution  is  here  under- 
stood its  volume  compared  with  that  of  water  con- 
taining the  same  total  number  of  molecules  at  the  same 
temperature;  in  the  experiments  it  was  18°  C.  By 
normal  solution  is  understood  a  solution  containing  one 
gram  equivalent  in  1000  grams  of  water. 

The  corresponding  values  for  the  constants  of  capil- 
larity of  1.5  normal  solutions  were  found  to  be: 

H     Diff.   NH«    Diff.     Li    Diff.    K    Diff.   Na 

I  113.14  -  .09  113.23  -.36  113.58  -.26  113.84 

NO3  109.75  -4.11  113.86  -  .36  114.22  +.30  113.92  -.33  114.25 

Br  110.40  -3.93  114.33  -  .10  114.43  -.25  114.68  -.05  114.73 

Cl  110.88  -3.60  114.48  -  .53  115.01  +.22  114.79  -.26  115.05 

OH  111.45  (+5.36)  106.81  (-8.40)  115.21  -.33  115.54  -.33  115.87 

112.49  (-3.42)  116.91  (-  .70)  117.61 

118.23  117.54 

-3.88       -  .27      -.09      -.25 

These  figures  are  very  instructive.  The  additive 
scheme  does  not  hold  for  all  the  solutions  examined,  as 
is  seen  from  the  figures  put  in  brackets.  It  is  necessary 
to  take  away  some  solutions,  especially  those  indicated, 
namely,  HOH,  NH4OH  and  ^H2S04,  in  order  to  find 
the  regularities  prevailing.  These  exceptions,  which 
caused  great  difficulty  for  the  pure  empirical  rule,  will 

8 


y»  THEORIES   OF   SOLUTIONS. 

be  seen  later  on  to  give  the  best  proof  of  the  applicability 
of  the  dissociation  theory. 

It  should  be  mentioned  that  Rontgen  and  Schneider 
emphasized  the  applicability  of  the  rule  of  additivity 
with  some  marked  exceptions — just  those  cited  above — 
but  did  not  feel  justified  to  conclude  that  a  dissociation 
of  the  salts  into  then*  ions  takes  place,  notwithstanding 
that  the  corresponding  theory  was  worked  out  par- 
tially before  the  authors  published  their  work  (1886). 

In  a  memoir  of  1885,  hi  which  Raoult  gives  the  final 
results  of  all  his  measurements  regarding  the  freezing 
points  of  salt  solutions,  he  comes  to  the  conclusion  that 
this  property  is  strongly  additive  in  regard  to  the  radi- 
cals of  which  the  salt  is  composed.  The  molecular 
lowering  of  the  freezing  point  might  be  calculated  as 
a  sum  of  the  lowerings  produced  by  the  constituent 
radicals.  For  each  negative  monovalent  radical,  such 
as  chlorine,  bromine,  hydroxyl,  CH3C02,  N03,  the  lower- 
ing is  20;  for  bivalent  negative  radicals,  such  as  S04, 
Cr04, 11;  for  monovalent  positive  radicals  such  as  H,  K, 
Na,  NH4,  15;  and  for  bi-  or  poly-valent  electropositive 
radicals,  such  as  Ba,  Mg,  A12,  8.  Thus  for  instance 
the  molecular  lowering  for  nitric  acid,  HN03  =  15  + 
20,  i.  e.,  35,  it  was  observed  to  be  35.8;  for  aluminium 
chloride,  A12C16,  it  is  calculated  to  be  8  +  6-20  =  128, 
found  129,  etc. 

Raoult  cites  some  other  investigations,  indicating  the 
additivity  of  different  properties  characteristic  for  salt 
solutions  and  then  continues:  "Then,  the  diminishing 
of  the  capillary  heights,  the  increase  of  the  densities, 
the  contraction  of  the  protoplast  (the  osmotic  pressure 
investigated  by  De  Vries),  the  lowering  of  the  freezing 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.  99 

point,  briefly  most  of  the  physical  effects  produced  by 
salts  on  the  water  dissolving  them  are  the  sum  of  effects  pro- 
duced separately  by  their  constituent  electropositive  and 
electronegative  radicals,  which  act  as  if  they  were  simply 
mixed  in  the  liquid. 

This  fact,  although  it  is  no  necessary  consequence 
of  the  dualistic  electrochemical  theory  of  the  salts, 
nevertheless  confirms  it  in  its  principle.  It  indicates 
that  the  salts  dissolved  in  water  should  be  regarded 
as  systems  of  particles,  of  which  everyone  is  composed 
of  solidary  atoms  and  retains,  unaffected  by  its  state 
of  combination  (e*tat  de  combinaison)  with  the  others, 
a  great  part  of  its  individuality,  its  action  and  its 
proper  characters." 

That  there  is  in  reality  no  question  of  a  real  dissocia- 
tion (it  is  even  said  that  the  particles,  i.  e.y  the  ions  are 
in  a  state  of  combination)  is  evident  from  the  fact  that, 
if  this  were  the  case,  all  the  radicals  ought  to  possess 
the  same  influence  on  the  depression  of  the  freezing 
point,  whereas  the  action  varies  between  20  and  8.  It 
is  also  clear  from  the  utterance  (1.  c.,  p.  406)  that  "the 
weak  acids  (such  as  HCN,  CH3C02H,  H2C204)  always 
give  an  abnormal  lowering  of  the  freezing  point  which 
is  about  only  half  the  normal  value,  as  if  the  majority 
of  their  molecules  were  united  two  and  two." 

There  is  also  a  great  number  of  other  anomalies 
summed  up  in  the  following  table: 

Salt.  Molecular  lowering  Ratio. 

Calculated.  Obseryed. 


Cu,  (CH3CO2)2 

8 

+  2-20=  48 

31.1 

1.54 

Pb,  (CH3C02)2 

8 

+  2-20=  48 

22.2 

2.16 

H,  (CH3C02) 

15 

+20      =  35 

19.0 

1.84 

A12,  (CH3CO2)6 

8 

+  6-20  =  128 

84.0 

1.52 

Fe*,  (CH3C02)6 

8 

+  6-20  =  128 

58.1 

2.20 

100          THEORIES  OF  SOLUTIONS. 


Salt.  Molecular  lowering  Batio. 

Calculated.  Observed. 


K,  SbO,  C^Ofl  2-15+11      =  41        18.4        2.23 

Hg,  Cla  8      +2-20=48        20.4        2.35 

Pt,  CU  8      +  4-20=  88        29.0        3.04 

Raoult  tries  to  explain  all  those  anomalies  by  suppos- 
ing that  double  or  triple  molecules  of  these  salts  are 
formed  in  their  solutions.  The  ratios  given  in  the  last 
columns  indicate,  according  to  Raoult's  method  of 
determination,  the  complexity  of  the  supposed  salt 
molecules.  It  varies  between  1.52  and  3.04.  In  reality 
there  is  a  great  number  of  minor  exceptions,  which  are 
not  so  very  easy  to  determine,  because  the  experimental 
errors  in  this  older  work  of  Raoult  are  rather  great. 

With  Raoult  's  memoir  of  1885  the  arguments  based 
upon  the  additive  properties  have  reached  their  highest 
point.  They  did  not  lead  to  the  hypothesis  of  a  real  dis- 
sociation, but  only  to  the  consequence  "that  the  salts 
(e.  g.,  NH4N03,  Na^SOO  should  be  regarded  as  systems 
of  particles  (in  these  cases  NH4  and  N03  or  2Na  and 
S04  respectively)  of  which  each  is  composed  of  solidary 
atoms  (i.  e.,  atoms  which  are  wholly  bound  to  each  other 
as,  e.  g.,  N  and  4H  in  NH4,  N  and  30  in  N03)  and  retains 
unaffected  by  its  state  of  combination  with  the  other 
(e.  g.,  S04  with  the  2Na)  a  great  part  of  its  individual- 
ity." This  is  exactly  the  theory  of  radicals,  according 
to  which  a  molecule  for  instance  of  alcohol  (C2H5OH) 
is  composed  of  radicals,  here  C2H5  and  OH,  which 
"unaffected  by  their  combination  with  each  other  re- 
tain a  great  part  of  their  individuality."  These  argu- 
ments could  never  lead  further,  because  of  the  many 
exceptions  stated,  which  are,  as  we  know  now,  due  to  a 
very  low  degree  of  dissociation.  The  non-conformity 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.         101 

of  these  arguments  to  fact  consists  in  supposing 
that  the  same  degree  of  independency  (dissociation) 
always  occurs  for  the  radicals,  whereas  hi  reality  the 
degree  of  dissociation  varies  from  very  nearly  zero  (in 
weak  acids  such  as  HCN)  up  to  nearly  unity  (strong 
acids  and  salts  of  monovalent  ions  in  high  dilution). 
As  we  know  now,  the  exceptions,  e.  g.y  water,  ammonia, 
sulphuric  acid,  from  the  rule  of  additivity  all  possess  a 
degree  of  dissociation  which  is  notably  different  from 
unity,  and  the  additivity  holds  strictly  only  for  com- 
pletely dissociated  salts  but  practically  for  such  as  are 
dissociated  to  about  80  or  90  per  cent. — the  agreement 
with  the  rule  being  the  greater  the  nearer  the  dissocia- 
tion is  to  unity. 

As  I  have  said  above,  E.  Wiedemann  has  adduced 
just  one  of  the  examples  of  additivity  cited  by  Valson 
to  show  that  the  dissociation  theory  is  false.  He 
argued  in  the  following  manner:  "If  we  replace 
chlorine  by  bromine  in  very  dilute  solutions  of  hydro- 
chloric acid  and  of  potassium  chloride,  the  quantity  of 
heat  developed  is  the  same  in  both  cases."  "Chlorine 
and  bromine  are  certainly  not  dissociated  at  common 
temperature."  The  same  is  valid  in  the  case  of  the 
displacement  of  chlorine  by  NOs  or  OH  in  dilute  solu- 
tion, in  which  case  we  have  to  calculate  the  heat  of 
formation  of,  e.  g.,  KN03  and  KOH  respectively  from 
their  elements  K,  N  and  30  or  K,  0  and  H  and  of  its 
following  solution  in  a  great  quantity  of  water.  This  is 
easily  done  by  aid  of  the  tables  given  by  thermo- 
chemists.  The  results  of  such  calculations  were  given 
by  myself  in  the  following  table,  giving  the  heat  of 
replacement  in  great  calories  (1000  cal.)  per  gram  equiv- 
alent. 


102          THEORIES  OF  SOLUTIONS. 


Max. 
H  K.  Na          Tl  Ca       %Sr       %Ba     Diff. 


C1-N08:  -19.9    -13.9  -13.7  -  9.6  -16.4  -17.6  -15.7  10.3 

NO3-Br:  +33.5    +24.4  +25.5  +16.9  +30.9  +31.0  +28.1  16.6 

Br-OH:  (-49.6)   -  8.1  -  6.1  -15.7  -37.0  -28.4  -22.5  30.9 

OH-I:  (+64.1)  +23.1  +32.8  +26.8  +53.7      —         —     30.6 

The  figures  regarding  water  are  put  in  brackets  because 
they  are  not  valid  for  a  very  dilute  aqueous  solution 
(but  for  concentrated  water)  and  therefore  do  not  agree 
with  the  conditions  demanded  by  Valson  and  Wiede- 
mann. 

Compare  this  table  with  the  following  one  of  the 
corresponding  heats  of  neutralization  of  strong  bases 
with  strong  acids  hi  dilute  solution,  adduced  by  myself 
in  favor  of  the  dissociation  theory: 

KOBE  NaOH  LiOH  KOH 

HC1,  HBr 

or  HI  13.75  13.75  13.9  13.8 

HNOi         13.8  13.7  13.7 

Max. 

%CaO,H,  %SrO,H2  %  BaO.H,  Diff. 

HC1,  HBr 

or  HI  14.0  14.1  13.85  0.35 

HNO,          13.9  13.9  13.9(14.15)        0.2  (0.45) 

The  figures  for  HC1,  HBr  and  HI  are  as  Berthelot 
has  tabulated  them.  For  J^Ba(OH)2  Berthelot  gives 
13.9,  Thomsen  14.15  —  without  doubt  the  figure  of  Ber- 
thelot is  the  probable  one.  All  the  figures  are  valid 
for  common  room  temperature  (18°  C.).  The  values 
given  in  the  last  column  are  the  differences  between 
the  smallest  and  the  greatest  figure  in  every  horizontal 
line.  This  maximal  difference  ought  to  be  zero  or 
fall  within  the  magnitude  of  experimental  errors  if 
perfect  additivity  prevailed,  as  is  really  the  case  for 
the  heat  of  neutralization,  but  not  at  all  for  the  heat 
of  displacement,  which  therefore  has  been  wrongly 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.         103 

cited  by  Valson  and  by  E.  Wiedemann  as  a  (nearly) 
additive  property. 

The  theory  proposed  by  Gay-Lussac  regarding  the 
"equipollency  "  of  salts  in  solution  is  the  first  one  (1839) 
that  reminds  us  of  the  theory  of  electrolytic  dissocia- 
tion. In  1850  Williamson  gave  a  theoretical  explana- 
tion of  the  fact  that  in  the  formation  of  ethyl  ether 
C2H5OC2H5  in  the  presence  of  sulphuric  acid,  H2S04,  this 
latter  is  not  consumed  by  the  chemical  process,  which 
therefore  is  a  catalytic  one  according  to  the  terminology 
proposed  by  Berzelius.  Williamson  expressed  the  opin- 
ion that  in  the  first  stage  C2H5.OH  and  H2.S04  exchange 
radicals  through  double  decomposition  so  that  HOH  and 
C2H6.H.S04  are  formed.  After  this  process  a  second  one 
takes  place  in  which  C2H6.H.S04  and  C2H5O.H  change 
radicals  through  double  decomposition  so  that  ethyl 
ether  C2H5O.C2H5  and  sulphuric  acid  H.H.S04  are 
formed.  The  total  change  due  to  the  two  processes  is 
therefore  a  formation  of  ethyl  ether  C2H5.O.C2H5  and 
water  H.O.H  from  two  molecules  of  alcohol  C2H6.O.H. 
The  quantity  of  sulphuric  acid  is  unchanged,  it  serves 
only  to  bind  the  water  formed  during  the  process.  It 
should  be  observed  that  C2H5OH  in  the  first  process  is 
decomposed  into  C2H5  and  OH,  in  the  second  one  into 
C2H50  and  H.  This  corresponds  to  fact. 

Williamson  generalized  this  idea  and  said  that  in  a 
solution  there  is  a  perpetual  change  of  radicals  between 
the  molecules.  In  this  way  the  fact  was  explained 
that,  in  mixing  two  salts  consisting  of  different  radicals, 
all  the  four  possible  salts  were  rapidly  formed  as  Gay- 
Lussac  maintained  (cf.  p.  75  above).  The  same  must 
also  be  true  regarding  molecules  of  similar  composition. 


104  THEORIES  OF  SOLUTIONS. 

Thus  for  instance  in  a  solution  of  hydrochloric  acid, 
H.C1,  an  atom  H  does  not  always  remain  bound  to  the 
same  atom  of  chlorine  but  exchanges  it  for  new  atoms 
of  chlorine,  the  one  after  the  other.  He  gives  still 
another  example:  if  we  mix  a  solution  of  Ag2S04  with 
one  containing  HC1,  then  some  few  molecules  of  H2S04 
and  AgCl  are  immediately  formed.  The  AgCl-mole- 
cules  are  very  slightly  soluble  and  precipitate  so  that 
HC1  and  Ag2S04are  not  formed  again.  But  new  mole- 
cules of  H2S04  and  AgCl  appear  in  the  solution  and 
the  newly  formed  AgCl  precipitates  again.  The  proc- 
ess goes  on  in  only  one  direction  until  there  remains 
only  such  a  small  quantity  of  AgCl  that  the  solution 
is  just  saturated  in  regard  to  it.  This  coincides  wholly 
with  the  theory  on  "equipollency"  of  salts  in  solution 
proposed  by  Gay-Lussac  in  1839. 

It  is  not  by  chance  that  Williamson  has  chosen  the 
electrolytes  (salts,  acids  and  bases)  as  example  of  his 
principle.  For  in  the  electrolytic  solutions  these 
changes  of  radicals — we  now  say  ions — go  on  instan- 
taneously as  hi  the  example  above.  All  attempts  to 
measure  the  velocity  of  reaction  in  cases,  when  elec- 
trolytes exchange  their  ions,  have  been  in  vain  on 
account  of  their  extreme  rapidity.  On  the  other  hand 
similar  reactions,  in  which  non-electrolytes  (or  perhaps 
better  stated  extremely  weak  electrolytes)  play  a  part, 
generally  proceed  slowly,  as  we  shall  also  see  later  in 
regarding  the  processes  characteristic  of  the  formation 
of  ethyl  ether. 

According  to  the  law  of  Faraday  each  monovalent 
ion  carries  a  charge  of  about  4.5. 10~10  electrostatic  units, 
the  positive  ions  as  H,  NH4,  K  and  generally  metals,  of 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.         105 

positive,  the  negative  ions  such  as  Cl,  CN,  N03,  C103, 
etc.,  or  generally  negative  radicals,  of  negative  elec- 
tricity. What  will  now  happen  if  we  place  a  solution 
containing  an  electrolyte  in  a  vessel  between  two  elec- 
trodes of  different  potential?  The  surface  of  the  fluid 
will  instantaneously  assume  a  charge,  so  that  positive 
ions  are  driven  against  the  negative  electrode  and  nega- 
tive ions  against  the  positive  one.  The  different  mole- 
cules will  therefore  be  turned  around  until  they  stand 
with  the  chlorine  ion  to  the  left  as  in  the  molecules  in 
the  figure  representing  this  case  (Fig.  2,  line  2).  Or  at 
least  a  majority  of  the  HC1  molecules  will  turn  their 
chlorine  to  the  left,  their  hydrogen  to  the  right.  In  the 
exchange  of  ions  between  the  HC1  molecules,  a  majority 


FIG.  2.    Grotthuss'  chain. 

of  the  chlorine  ions  will  wander  to  the  left,  the  majority 
of  the  hydrogen  ions  to  the  right.  Then  they  carry  their 
charges  with  them  and  the  said  movement  of  the  ions 
corresponds  to  a  transporting  of  positive  electricity  in 
the  direction  of  the  arrow  from  left  to  right.  Negative 
electricity  wanders  from  the  right  to  the  left,  which  is 
equivalent  to  a  wandering  of  positive  electricity  in  the 
opposite  direction.  This  is  about  the  position  taken  by 
Grotthuss  as  early  as  1825  and  represented  by  Fig.  2. 


106  THEOKIES   OF   SOLUTIONS. 

It  is  just  this  latter  idea  which  has  been  developed 
by  Clausius  in  a  memoir  of  1857  without  a  knowledge  of 
Gay-Lussac's  or  Williamson's  paper.  Clausius  tried 
to  explain  how  the  law  of  Ohm  may  hold  for  electro- 
lytic solutions,  which  had  been  proved  by  experiment. 
Ohm's  law  demands  that  even  the  least  electric  force 
causes  a  motion  of  the  ions.  Hence  if  these  were 
bound  to  each  other  in  the  electrolytic  molecule,  so  that 
a  certain  force  were  necessary  to  tear  them  asunder, 
as  was  and  is  generally  believed  amongst  chemists, 
just  this  minimum  of  electric  force  (slope  of  potential) 
would  be  necessary  for  establishing  an  electric  current; 
this  is  in  contradiction  to  Ohm's  law.  Clausius  drew 
the  conclusion  that  the  ions  in  electrolytic  molecules  are 
not  fixed  to  each  other,  but  might  be  exchanged  for 
ions  from  other  molecules  just  as  Williamson  had 
supposed.  "The  frequency  of  such  mutual  decomposi- 
tion depends  upon  two  circumstances,  firstly  on  the 
greater  or  less  coherence  of  the  ions  with  each  other 
and  secondly  on  the  violency  of  the  molecular  move- 
ment, i.  e.,  on  the  temperature." 

Clausius  also  considers  the  theory  of  Williamson  to 
which  a  chemist  had  directed  his  attention  and  says 
that  "Williamson  speaks  of  a  perpetual  change  of  the 
hydrogen  atoms  (between  the  HC1  molecules),  whereas 
for  the  explanation  of  the  conduction  of  electricity  it 
suffices  that  at  the  collisions  of  the  molecules  now  and 
then,  and  perhaps  relatively  seldom,  an  exchange  of  the 
partial  molecules  (i.  e.,  ions)  takes  place." 

"The  increase  of  conductivity  with  temperature  is 
explained  in  an  unconstrained  way  by  this  theory," 
Clausius  says,  "because  the  greater  violence  of  the 


THEORY  OF  ELECTROLYTIC   DISSOCIATION.         107 

molecular  movement  must  contribute  to  an  increased 
reciprocal  decomposition  of  the  molecules." 

Of  course  it  must  be  regarded  as  very  much  strength- 
ening the  hypothesis  of  mutual  exchange  that  three 
leading  scientists,  of  whom  two  were  chemists  and  the 
third  a  physicist,  from  apparently  quite  different  empir- 
ical premises  have  been  led  to  the  same  conclusion,  and 
therefore  it  seems  just  to  attach  the  names  of  all  three 
of  them  to  their  hypothesis.  The  form  given  to  it  by 
Gay-Lussac  and  Williamson  corresponds  better  to  our 
present  knowledge.  A  " perpetual  exchange"  comes 
much  nearer  to  real  dissociation  than  an  "exchange 
now  and  then."  Further,  there  have  been  objections 
against  Clausius  that  according  to  his  theory  the  con- 
ductivity should  be  proportional  to  the  number  of 
collisions  of  electrolytic  molecules,  i.  e.,  to  the  square  of 
their  concentration,  whereas  it  really  increases  more 
slowly  than  in  proportion  to  this  quantity.  Also  the 
explanation  of  the  increase  of  conductivity  with  tem- 
perature, given  by  Clausius,  has  not  proved  successful. 
In  most  cases  the  degree  of  dissociation  decreases  a 
little  with  increasing  temperature,  and  the  increased 
conductivity  depends  upon  the  diminishing  of  the 
internal  friction  with  temperature. 

The  renowned  Italian  physicist  Bartoli  has  expressed 
a  similar  theory,  where  dissociation  is  spoken  of  directly, 
in  the  year  1882.  He  investigated  the  so-called  residual 
current,  which  is  observed  to  pass  through  an  electro- 
lyte, even  if  the  electromotive  force  necessary  for  its 
decomposition  is  not  reached.  Bartoli  gives  two 
different  theories  for  the  explanation  of  the  residual 
current.  Either  the  polarization,  which  hinders  elec- 


108  THEORIES  OF  SOLUTIONS. 

trolysis,  disappears  slowly  by  means  of  diffusion  of  the 
polarizing  substances  from  the  electrodes,  or  there  is  a 
dissociation  of  the  electrolytic  molecules.  The  first 
theory  is  generally  accepted  as  the  right  one  and  was 
already  at  that  tune  after  Helmholtz's  and  Witkowski's 
important  investigations  (1880).  The  second  one  fur- 
ther demands  that  the  degree  of  dissociation  is  pro- 
portional to  the  third  power  of  the  acting  electromotive 
force,  that  is,  if  no  electromotive  force  acts,  it  is  zero 
(to  the  third  power),  and  this  case  is  just  the  one  for 
which  the  modern  dissociation  theory  demands  a  high 
degree  of  dissociation,  which  is  further  independent  of 
the  acting  electromotive  force,  if  there  is  such  a  one. 
The  claims  of  priority  raised  by  Bartoli  in  1892  regard- 
ing the  theory  of  electrolytic  dissociation  can  therefore 
not  seriously  be  discussed.  It  ought  well  be  said  that 
it  would  have  been  much  more  adequate  if  he,  like  his 
predecessors,  from  Gay-Lussac  to  Valson  had,  refrained 
from  drawing  such  a  wide-reaching  conclusion,  as  that 
salts  are  dissociated,  from  such  a  small  number  of  facts. 
In  1883  I  investigated  the  conductivity  of  electro- 
lytes as  depending  on  their  concentration  and  tempera- 
ture and  came  to  the  conclusion  (published  1884)  that 
their  solutions  contain  two  different  kinds  of  molecules, 
of  which  the  one  is  a  non-conductor,  the  other  conduct- 
ing electricity  in  consequence  of  properties  attributed 
to  it  by  the  hypothesis  of  Gay-Lussac,  Williamson  and 
Clausius.  These  latter  were  simply  called  active  mole- 
cules. The  number  of  active  molecules  increases  with 
dilution  at  the  expense  of  the  inactive  ones  and  tends 
to  a  limit,  which  is  probably  first  reached  when  all 
inactive  molecules  have  been  transformed  into  active 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.         109 

ones.  At  very  high  dilutions  the  additive  property 
of  the  conductivity  postulated  by  Kohlrausch  is  not 
only  true  within  certain  groups  of  electrolytes  of  similar 
composition  but  for  all  electrolytes  of  whatsoever  com- 
position. An  acid  is  the  stronger  the  greater  its  con- 
ductivity is.  At  infinite  dilution  all  acids  have  the 
same  strength.  These  assertions  were  demonstrated 
to  be  in  accord  with  the  thermochemical  measurements 
of  Berthelot  and  Thomsen.  Similar  rules  are  valid  for 
bases.  Chemical  activity  therefore  coincides  with  elec- 
trical activity.  Water,  alcohols,  phenols,  aldehydes, 
etc.,  which  exchange  ions  with  electrolytes  are  also 
electrolytes.  The  relative  conductivity  of  water  in- 
creases more  rapidly  with  temperature  than  that  of 
acids,  bases  or  salts.  Therefore  the  hydrolysis  of  salts 
increases  with  temperature.  The  results  of  Thomsen's, 
Guldberg's  and  Waage's,  and  especially  of  Ostwald's 
measurements  of  chemical  equilibria  were  discussed  and 
their  discrepancies  with  Guldberg  and  Waage's  law 
explained  as  dependent  on  the  lowering  of  the  activity 
of  the  examined  weak  acids  caused  by  the  presence  of 
their  salts  and  of  strong  acids.  The  heat  evolved  in  the 
neutralization  of  a  wholly  active  acid  with  a  wholly 
active  base  is  always  the  same  and  equal  to  the  heat 
which  is  consumed  in  the  activation  of  an  equivalent 
quantity  of  water.  The  deviation  of  the  heat  of  neu- 
tralization of  weak  acids  or  weak  bases  from  the  said 
value  is  due  to  the  heat  necessary  for  their  activation. 
In  a  reaction  of  ferrocyanide  of  potassium  K4.C6N6Fe, 
the  ions  of  which  are  4K  and  the  rest,  with  other 
electrolytes,  ferrocyanides  and  potassium-salts  are  al- 
ways formed  but  not  ferrous  or  ferric  salts,  because  there 


110          THEOKIES  OF  SOLUTIONS. 

occurs  only  a  rearrangement  of  the  ions.  Therefore 
the  ion  contained  in  the  ferrocyanides  cannot  be  de- 
tected by  means  of  ordinary  reagents  on  iron,  which  are 
all  electrolytes. 

When  this  memoir  was  written  (1883)  the  measure- 
ments of  Raoult  on  the  freezing  point  of  salt  solutions 
had  not  appeared.  Therefore  it  was  regarded  as  too 
bold  to  state  verbally  that  the  active  molecules  were 
dissociated  into  their  ions  and  it  was  only  maintained 
that  they  should  be  subject  to  the  conditions  demanded 
by  the  hypothesis  of  equipollency.  Soon  afterwards 
Raoult's  aforementioned  measurements  were  published 
and  their  theory  given  by  van't  Hoff  (1885).  Im- 
mediately after  that  I  calculated  the  coefficient  of 
activity  from  the  conductivity  figures  and  the  degree 
of  dissociation  which  was  necessary  to  explain  the  values 
i  of  van't  Hoff,  calculated  from  Raoult's  data.  A  very 
good  agreement  was  found  and  then  the  basis  for  an 
open  declaration  of  the  state  of  dissociation  of  elec- 
trolytes was  found  strong  enough  (1887).  The  word 
activity  was  replaced  by  the  word  electrolytic  dissocia- 
tion. 

Immediately  after  my  memoir  of  1884  had  appeared, 
Ostwald  carried  out  a  great  number  of  measurements, 
showing  that  the  velocity  of  reaction,  when  different 
acids  exert  a  catalytic  action,  is,  as  my  theory  de- 
manded, nearly  proportional  to  their  conductivity,  and 
further  that  the  relative  strength  of  weak  acids  increases 
with  dilution.  In  1889  I  showed  that  the  catalytic 
action  of  different  acids  on  inverting  cane  sugar,  if  it  is 
corrected  for  the  so-called  salt-action,  is  proportional 
to  the  concentration  of  the  hydrogen-ions  present. 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.         Ill 

Ostwald,  Planck  and  van't  Hoff  and  Reicher  simul- 
taneously and  independently  of  each  other  applied  the 
law  of  mass-action  on  the  equilibrium  between  ions  and 
undissociated  molecules  of  an  electrolyte  (1888).  Ost- 
wald found  that  this  law  really  holds  good  for  weak 
acids.  Van't  Hoff  and  Reicher  were  not  content  with 
the  figures  already  published  regarding  the  conductivity 
of  weak  acids  and  therefore  they  performed  extremely 
accurate  redeterminations,  which  gave  an  excellent 
agreement  with  the  demands  of  the  said  law,  which  was 
called  for  this  special  case  Ostwald's  law.  Planck 
finally  did  not  succeed  with  the  application  of  this 
law  to  salts,  and  this  disagreement  for  strongly  dis- 
sociated electrolytes  still  persists.  Later  on  (1894) 
Bredig  proved  that  Ostwald's  law  is  valid  also  for  weak 
bases. 

From  the  law  of  van't  Hoff  regarding  the  change  of 
chemical  equilibria  with  temperature  (cf .  p.  83  and  84)  I 
calculated  the  heat  of  electrolytic  dissociation  of  differ- 
ent weak  acids  and  showed  it  to  be  in  perfect  agreement 
with  the  observed  heats  of  neutralization.  Kohlrausch 
and  Heydweiller  did  the  same  work  for  the  most  im- 
portant and  most  difficultly  determined  of  all  examined 
electrolytes,  namely  water.  In  two  new  memoirs  I  de- 
termined the  general  laws  of  equilibrium  between  elec- 
trolytes. Ostwald  demonstrated  the  extreme  useful- 
ness of  the  new  theory  for  general  and  analytical 
chemistry.  (1900  and  1904.) 

The  chief  points  of  the  theory  of  electrolytic  dissocia- 
tion were  then  fixed. 


LECTURE  VII. 

VELOCITY  OF  REACTION. 

THE  first  velocity  of  reaction  studied  was  that  on 
the  inversion  of  cane-sugar  investigated  by  Wilhelmy, 
in  the  year  1850.  This  process  has  a  great  practical 
use,  as  the  determination  of  the  quantity  of  cane  sugar 
in  a  solution  depends  upon  it.  Wilhelmy  used  the 
saccharimeter  of  Soleil,  the  same  instrument  which  was 
in  use  in  the  sugar-factories.  It  was  known  that  the 
hydrolysis  (decomposition  with  addition  of  water)  of 
cane  sugar  may  be  carried  out  at  low  temperatures  if 
an  acid  was  added  to  the  sugar  solution.  It  was  the 
velocity  of  this  latter  reaction,  which  was  a  typical 
example  of  what  Berzelius  called  catalytic  processes, 
that  was  the  object  of  Wilhelmy 's  investigation.  He 
stated  that  temperature  exerts  a  great  influence,  he 
therefore  tried  to  carry  out  his  experiments  at  a  not 
too  variable  temperature  by  placing  his  vessels  con- 
taining the  solutions  of  cane-sugar  in  a  large  vessel  of 
water,  heated  by  a  spirit  flame  of  constant  size,  or  at 
lower  temperature  in  a  very  large  heat-isolated  vessel 
filled  with  water. 

Wilhelmy  found  that  the  general  law,  which  holds 
for  the  fall  of  temperature  to  that  of  the  surrounding 
temperature  (Newton)  or  for  the  loss  of  electricity  from 
a  charged  conductor  (Coulomb),  is  also  true  for  the  trans- 
formation of  cane  sugar,  namely  that  the  transformed 

quantity  in  a  given  short  time  is  proportional  to  the 

112 


VELOCITY  OF  REACTION.  113 

remaining  quantity.  The  strong  acids :  sulphuric,  hydro- 
chloric, nitric  and  phosphoric  were  found  to  be  effective, 
but  acetic  acid  had  no  appreciable  influence  (in  fact 
it  gives  the  same  effect  as  the  strong  acids,  but  after 
a  much  longer  time). 

As  an  example  we  cite  some  experiments  with  nitric 
acid  at  15°  C. 

Time  of  A -x  ,        ^  g_  I  loff     A 

Reaction  (Min. ).     Quant .  Sugar.  log  A  —  x '  ~  t     g  A  -  x ' 


0  65.45 


45  56.95  0.0605  0.00134 

90  49.45  0.1217  0.00135 

150  40.70  0.1981  0.00132 

210  33.70  0.2880  0.00137 

270  26.95  0.3851  0.00142 

The  time  law  proposed  by  Wilhelmy  leads  to  the 
expression 

log  A  -  log  (A  -  x)  =  Kt, 

where  t  is  the  time  of  reaction,  x  the  quantity  of  trans- 
formed sugar  after  that  time,  A  the  quantity  of  sugar 
present  at  the  beginning  and  K  a  constant.  The  for- 
mula expresses  very  well  the  progress  of  the  process;  it 
has  been  confirmed  later  by  a  great  number  of  in- 
vestigators. 

It  is  possible  to  invert  the  cane  sugar  without  the 
addition  of  acids  at  higher  temperatures,  e.  g.,  in  auto- 
claves above  100°  C.  Of  course  this  process  goes  on 
also  at  low  temperatures  but  so  slowly  that  it  cannot 
conveniently  be  measured.  The  same  process  is  also 
promoted  by  an  enzyme  called  invertase,  which  is  pro- 
duced by  yeast  cells.  It  was  believed  for  a  long  tune, 
according  to  experiments  performed  by  V.  Henri,  that 
this  process  obeys  another  time  law  than  that  relating 
to  inversion  by  means  of  acids.  Hudson  has  shown 

9 


114  THEORIES  OF  SOLUTIONS. 

that  the  exceptional  behavior,  found  by  Henri,  de- 
pends upon  the  abnormal  rotatory  power  (the  so-called 
mutarotation)  of  the  components  of  invert  sugar,  when 
they  are  recently  formed.  The  values  of  x,  i.  e.,  the 
transformed  quantity  of  sugar,  were  therefore,  in 
Henri's  determinations,  affected  by  great  errors.  It  is 
possible  to  avoid  this  error  by  adding  a  trace  of  alkali 
to  the  solution  of  invert  sugar,  which  very  rapidly 
reaches  its  end  value  of  rotating  power  under  such 
circumstances.  When  these  measures  are  taken,  the 
change  of  cane  sugar  by  means  of  invertase  goes  on 
according  to  the  same  law  as  if  it  were  promoted  by 
acids.  This  observation  is  very  important  as  it  shows 
again  that  the  supposed  difference  in  action  of  organic 
products  (enzymes)  and  inorganic  substances  (acids) 
is  not  a  real  one.  It  is  to  be  hoped  that  the  correspond- 
ing irregularity  found  by  Henri,  his  pupils,  and  others 
in  the  transformation  of  other  sugars,  will  also  disap- 
pear on  closer  investigation.  This  has  already  been 
proved  by  A.  E.  Taylor  regarding  the  hydrolysis  of 
maltose  by  means  of  maltase  and  that  of  starch  with 
salivary  amylase.  That  the  inversion  caused  by  means 
of  acids  goes  on  regularly  depends  upon  the  destruction 
of  mutarotation  by  acids,  which  is  not  quite  so  rapid 
as  that  of  alkalies,  but  still  sufficient  to  prevent  serious 
disturbances. 

The  said  hydrolysis  is  also  caused  by  ultra-violet 
light.  Most  reactions,  especially  hydrolytic  ones,  pos- 
sess the  same  peculiarity  as  the  inversion  of  cane-sugar 
in  that  they  are  catalyzed  by  hydrogen  or  hydroxyl  ions 
(i.  e.,  by  the  presence  of  acids  or  bases)  and  by  special 
enzymes.  High  temperature  or  ultraviolet  light  act 


VELOCITY  OP  REACTION.  115 

in  the  same  manner.  In  the  yeast  cells  there  is  another 
enzyme,  zymase,  which  carries  the  process  further 
when  cane-sugar  has  been  transformed  to  glucose. 
Zymase  transforms  it  to  alcohol  and  carbonic  acid; 
probably  lactic  acid  is  an  intermediary  stage.  On  the 
other  hand  Duclaux  showed  that  glucose  in  the  presence 
of  potassium  hydrate  or  ammonia  (i.  e.  hydroxyl  ions) 
in  sunlight  gives  alcohol  and  C02.  If  Ba(OH)2  was 
used  as  the  alkali  the  process  went  on  only  as  far  as  the 
formation  of  lactic  acid,  which  by  the  means  of  potas- 
sium hydrate  and  sunlight  could  further  on  change  to 
alcohol  and  C02.  Buchner  and  Meisenheimer  found 
that  sunlight  is  not  absolutely  necessary.  They  boiled 
inverted  cane-sugar  with  strong  KOH  and  thus  pro- 
duced alcohol  without  sunlight.  Nencki  and  Sieber 
stated  that  glucose  with  0.3  per  cent.  KOH  gives  lactic 
acid  after  10  days  at  35-40°  C.  Hanriot  continued 
this  process  by  boiling  calcium  lactate  with  calcium 
hydrate  and  obtained  alcohol,  just  as  Duclaux  by  means 
of  sunlight. 
We  have  here  a  number  of  reactions,  namely: 

1)  CuH^On  +  H2O  =  C6H12O6  +  C6H1206  (catalyzer 

cane  sugar          water          glucose  laevulose 

H-ions  or  invertase  or  light). 

2)  CeH^Oe  =  2CH3CHOHCOOH   (catalyzer  OH-ions 

glucose  lactic  acid 

or  light  or  yeast). 

3)  C3H603  =  C2H6OH  +  C02  (catalyzer  OH-ions  or 

lactic  acid  alcohol      carbonic  acid 

light). 

Evidently  in  Duclaux's  experiments  with  Ba(OH)2 


116  THEORIES  OF  SOLUTIONS. 

the  process  was  brought  to  a  relative  standstill  because 
of  the  slight  solubility  of  the  barium  lactate,  when 
this  intermediary  product  had  been  formed. 

Other  hydrolytic  processes  of  very  high  importance, 
which  are  accelerated  by  hydroxyl  or  hydrogen  ions 
and  by  special  enzymes,  namely  trypsin  and  pepsin,  are 
the  so  called  digestive  processes.  The  most  important 
natural  process,  namely  the  formation  of  sugar  from 
carbonic  acid  and  water  by  the  means  of  the  catalytic 
action  of  the  chlorophyll  in  the  green  parts  of  plants, 
probably  takes  place  through  a  previous  formation  of 
formaldehyde,  HCOH,  and  oxygen  (O2)  from  CO2  and 
H20.  It  has  recently  been  found  possible  to  reproduce 
this  photochemical  process  without  the  help  of  living 
organisms  (D.  Berthelot,  Stoklasa). 

In  many  cases  the  process  itself  produces  a  substance 
which  accelerates  it.  Thus  for  instance  if  we  dissolve 
copper  in  nitric  acid,  nitrous  acid  i  formed,  which 
accelerates  the  solution.  Therefore  if  we  put  pieces  of 
copper  in,  say  10  per  cent.,  pure  nitric  acid,  the  copper 
is  at  first  very  slowly  attacked;  but  the  velocity  of 
reaction  increases  so  that  after  a  tune  the  reaction  is 
violent,  giving  rise  to  a  strong  current  of  gas-bubbles. 
Such  a  process  is  the  inversion  of  cane-sugar  without 
acids  at  high  temperatures.  The  cane  sugar  itself  has  a 
weak  acid  reaction,  but  its  hydrolytic  products,  glucose 
and  still  more  laevulose  have  much  stronger  acid 
properties  as  Madsen  found.  Therefore  the  reaction 
goes  on  with  accelerated  velocity,  until  finally  very  little 
cane-sugar  is  left,  so  that  the  process  becomes  complete 
by  degrees.  Such  an  "autocatalytic"  process  is  also  the 
saponification  of  an  ester,  e.  g.,  ethyl  acetate  by  means 


VELOCITY  OF  REACTION.  117 

of  water.  At  first  the  hydroxyl  ions  of  the  water  pro- 
duce saponification  just  as  bases.  The  product,  acetic 
acid,  diminishes  the  quantity  of  the  hydroxyl  ions,  so 
that  the  process  goes  on  more  slowly.  But  the  hydro- 
gen ions  of  the  acetic  also  cause  a  saponification  al- 
though they  are  not  so  active  as  the  hydroxyl  ions  (they 
act  140  times  less),  and  when  they  have  increased  to  a 
sufficient  number  the  process  is  accelerated  after  it 
has  passed  through  a  minimum,  when  the  hydrogen- 
ions  are  140  times  as  many  as  the  hydroxyl-ions.  This 
reaction  has  been  studied  by  Wijs,  who  found  that  the 
experiment  wholly  confirmed  the  theory. 

Even  the  common  growth  of  organisms,  e.  g.,  bacteria, 
has  been  regarded  as  such  an  autocatalytic  process. 
If  bacilli,  e.  g.,  coli  bacilli,  are  inoculated  into  a  solution, 
containing  their  nourishment  with  a  certain  quantity 
of  oxygen  over  it,  and  the  whole  is  shaken  so  that 
oxygen  is  continuously  carried  to  the  bacilli,  these  are 
first  increased  in  number,  each  independent  of  the 
others,  so  that  the  number  of  bacilli  increases  according 
to  an  exponential  function,  which  as  the  curve  shows  is 
suddenly  broken  down,  when  the  oxygen  or  nourishment 
begins  to  be  nearly  consumed.  This  phenomenon  has 
been  studied  in  my  laboratory  by  Mr.  Thor  Carlson. 

The  growth  of  a  single  organism  shows  similar  pecu- 
liarities. To  begin  with  the  increase,  measured  by 
weight,  becomes  greater  and  greater,  then  it  is  nearly 
constant,  and  thereafter  decreases. 

A  very  important  case  of  reactions  which  are  ham- 
pered by  their  own  reaction  products  has  been  studied 
by  me.  If  ammonia  acts  upon  ethyl  acetate,  which  is 
supposed  to  be  present  in  great  excess  so  that  its  quan- 


118  THEOEIES  OF  SOLUTIONS. 

tity  may  be  regarded  as  constant,  then  the  velocity  of 
reaction  is  proportional  to  the  number  of  hydroxyl  ions 
present.  The  progress  of  the  reaction  is  followed  by 
means  of  the  conductivity  of  the  ammonium  acetate 
formed.  Now  the  number  of  hydroxyl  ions  is  almost 
inversely  proportional  to  the  quantity  of  ammonium 
acetate  already  formed  and  therefore  the  velocity  of 
reaction  is  also  inversely  proportional  to  the  said  quan- 
tity. This  leads  to  the  differential  equation 

dx     K(A-x) 
dt'         x        ' r' 

where  A  is  the  quantity  of  ammonia  present  from  the 
beginning,  x  the  quantity  of  ammonium  acetate  formed, 
K  a  constant  and  P  the  quantity  of  ethyl  acetate  which 
may  also  be  regarded  as  a  constant.  When  x  is  small 
compared  with  A  we  obtain: 

xdx  =  KAPdt 
or  integrated: 

x2  =  2KA  .P.t. 

This  formula  tells  us  that  the  reaction  proceeds  so  that 
the  quantity  of  ammonium  acetate  is  proportional  to 
the  square  root  of  the  time  and  also  of  the  quantities 
of  ethyl  acetate  (substrate)  and  reagent  (ammonia). 
The  truth  of  this  premise  is  seen  from  the  following 
figures,  found  for  0.66  n.  ethyl  acetate  at  14.8°  C. 

t  zobs.  x  calc.  17.3  Vf  t  x  obs.  x  calc.  17.3  Vj 

1  17.5  19.4  17.3  10  51.2  51.3  54.7 

2  25.5  25.2  24.5  15  59.6  59.7  67.0 

3  30.7  30.6  29.9  22  67.5  68.6  81.1 

4  34.7  34.9  34.6  30  74.5  74.7  94.7 
6  41.5  41.7  42.4  40  80.7  80.7  109.4 
8  47.0  46.9  48.9  60  88.2  88.2  134.0 


VELOCITY  OF  REACTION.  119 

The  time  i  is  given  in  minutes,  x  in  per  cent.  The 
column  17.3  V  t  agrees  well  with  x  obs.,  until  this  exceeds 
50  p.  c.  After  that  the  x  calculated  found  according 
to  the  exact  integral  of  the  last  differential  equation 
holds  good. 

The  said  rule  that  the  transformed  quantity  is  pro- 
portional to  the  square  root  of  the  acting  quantity  and 
time  is  called  Schiitz's  rule  and  holds  for  a  great  number 
of  reactions  in  physiological  chemistry,  amongst  others 
digestion  by  means  of  pepsin  or  of  trypsin,  the  hydro- 
lytic  action  of  Upases  on  fats,  etc.  As  an  instance  some 
figures  given  by  Schiitz  may  serve  for  the  quantity 
formed  in  the  action  of  different  quantities  of  pepsin  at 
37.5°  C.  on  the  same  quantity  of  egg-albumen,  freed 
from  globulin. 

Quantity  of  Pepsin  P.     1         4  9  16  25  36  49  64 

Quantity  of  peptone 

found  _  9.4  20.6  32.3  45.4  55.2  65.0  76.0  85.3 

10.8  Vp  10.8  21.6  32.4  43.2  54.1  64.9  75.7  86.5 

Experiments  regarding  the  influence  of  time  are  given 
by  Sjoqvist  for  peptic  digestion,  by  Stade  for  the  lipo- 
lytic  action  of  gastric  juice  and  by  others.  The  agree- 
ment with  the  exact  formula  is  in  most  cases  very 
satisfactory. 

In  this  case  the  expression  Pt  enters  into  the  final 
formula.  Therefore  the  same  quantity  of  reaction- 
product  is  produced  by  the  enzyme  quantity  q  in  1  hour 
as  by  the  quantity  1  acting  during  q  hours  on  the  same 
quantity  of  substance.  In  many  investigations  of  a 
physiological-chemical  nature,  it  is  easy  to  determine 
a  certain  point  of  decomposition,  e.  g.,  when  milk 
coagulates,  when  peptization,  i.  e.,  liquefaction  of  gels 


I 
120          THEORIES  OF  SOLUTIONS. 

is  reached,  etc.  In  such  cases  it  is  generally  stated  that 
the  necessary  time  is  inversely  proportional  to  the 
quantity  of  enzyme  adapted  to  the  experiment. 

I  have  laid  so  very  great  stress  upon  the  fact  that 
we  may  find  Schiitz's  rule  to  hold  good  for  simple 
inorganic  processes,  also  because  at  an  earlier  stage  it 
was  maintained  that  this  rule  was  peculiar  to  the  action 
of  ferments  in  contradistinction  to  catalyzers,  which  are 
not  prepared  by  living  organisms.  The  deduction  of 
this  rule  indicates  that  it  is  applicable,  as  soon  as  one 
of  the  reaction  products  reacts  with  the  catalyzer,  so 
that  the  free  quantity  of  this  substance  is  nearly  in- 
versely proportional  to  the  quantity  of  reaction  pro- 
ducts. The  deduction  has  also  given  a  formula  which 
holds  for  any  magnitude  of  the  transformed  quantities 
whereas  the  rule  of  Schtitz  is  not  reliable  for  higher 
values  of  x  than  about  50  per  cent. 

As  we  have  seen  before,  Williamson  explained  the  pe- 
culiar action  of  catalyzers  by  stating  that  they  give  inter- 
mediary products  of  reaction  from  which  the  catalyzer 
is  formed  again  in  a  later  chemical  reaction.  Thus  for 
instance,  according  to  Williamson,  the  sulphuric  acid 
in  the  formation  of  ethyl  ether  from  alcohol  at  first 
gives  ethyl  sulphuric  acid  C2H5HSO4,  which  thereafter 
reacts  with  alcohol  to  give  back  sulphuric  acid  and  form 
ether.  The  two  steps  of  this  reaction  are  the  following : 

1)  C2H5OH  +  H2S04  =  C2H5HS04  +  H20, 

2)  C2H5HS04  +  C2H6OH  =  C2H6OC2H8  +  H2S04, 
or  taken  together: 

2C2H5OH  =  C2H5OC2H6  +  H20. 


VELOCITY   OF  KB  ACTION.  121 

In  reality  the  process  is  a  dehydration  of  the  alcohol 
and  depends  upon  the  binding  of  H20  to  the  sulphuric 
acid.  Therefore  the  process  is  very  much  retarded 
when  a  considerable  quantity  of  water  has  been  formed. 

This  process  has  been  investigated  by  Kremann.  He 
found  that  reaction  1  goes  on  rather  rapidly  at  moderate 
temperatures  and  in  the  absence  of  water,  the  constant 
of  reaction  being  0.00112  at  40°  and  0.0044  at  51°, 
corresponding  to  an  increase  in  the  proportion  1  to  3.63 
in  an  interval  of  10°  C.  The  velocity  constant  of  the 
formation  of  C2H5HSO4  is  about  1.7  times  greater  than 
that  of  its  decomposition.  In  aqueous  solution  the 
velocity  constants  are  about  50  times  less  (investigated 
for  the  decomposition  of  C2H5HS04)  and  their  increase 
in  an  interval  of  10°  C.  about  as  1  to  1.99.  Hence  we 
conclude  that  the  reaction  is  hampered  in  a  high  degree 
by  the  presence  of  water  and  that  in  the  higher  degree 
the  lower  the  temperature  is.  Reaction  2  is  inappreci- 
able at  low  temperatures  and  can  only  be  investigated 
above  100°  C.  Its  velocity  sinks  very  rapidly  with  the 
increase  of  the  water  formed.  Its  rate  of  increase  with 
temperature  is  in  about  the  proportion  of  1  to  2.35 
in  an  interval  of  10°  C.  at  117.5°. 

The  velocity  of  the  total  reaction  is  determined  by 
the  slow  one,  i.  e.,  the  second  one,  of  the  two  partial 
reactions.  In  any  case  Kremann  has  shown  that 
Williamson's  theory  of  the  formation  of  ether  is  correct. 

The  said  process  is  a  very  complicated  one.  There 
are  some  other  compound  processes,  which  show  a 
greater  regularity.  Amongst  those  the  radioactive 
changes,  which  are  independent  of  temperature  and 
concentration,  have  been  very  closely  studied,  especi- 


122          THEORIES  OF  SOLUTIONS. 

ally  by  Rutherford.  In  some  cases,  as  with  the  radio- 
active deposit  from  actinium  emanation,  the  velocity 
of  reaction  characteristic  of  the  two  consecutive  proc- 
esses are  very  different  from  each  other,  the  actinium 
A  being  decomposed  to  50  per  cent,  hi  35.7  minutes, 
whereas  the  corrresponding  time  for  actinium  B  is 
2.15  minutes.  Then  the  total  process  except  at  the 
very  beginning  may  be  regarded  as  a  reaction  going 
on  with  the  velocity  of  the  first  reaction.  In  other 
cases  as  with  the  decay  of  the  excited  activity  from 
radium  emanation  there  are  products,  radium  A,  radium 
B,  and  radium  C,  which  do  not  differ  so  very  much 
from  each  other  in  their  rate  of  decay,  the  correspond- 
ing times  being  3,  21  and  28  minutes  respectively.  In 
this  case  the  total  decay,  measured  by  means  of  the 
emitted  (0  or)  7  rays,  which  accompany  the  decom- 
position of  radium  C,  gives  totally  different  time  curves, 
according  to  the  time  during  which  the  radioactive 
deposit  has  been  formed.  Through  a  thorough  exam- 
ination of  the  different  possible  cases,  the  different  proc- 
esses have  been  separated  from  each  other  and  the  rate 
of  decay  for  each  of  them  determined. 

Probably  the  effect  of  catalyzers  depends  in  most 
cases,  just  as  in  the  case  of  the  formation  of  ether,  on 
their  entering  into  intermediary  chemical  reactions 
from  which  they  are  regenerated  hi  later  reactions. 
In  some  cases  as  with  platinum  sponge,  or  with  cata- 
lyzers in  suspension  the  effect  is  probably  due  to  an 
adsorption  of  the  reagents  on  the  catalytic  agent. 

It  is  well  known  that  van't  Hoff  introduced  the  notion 
monomolecular,  bimolecular,  etc.,  reactions  according 
to  the  number  of  molecules  which,  represented  by  the 


VELOCITY  OF  KEACTION.  123 

chemical  equation  react  upon  each  other,  and  for  each 
of  them  a  certain  equation  of  reaction  is  character- 
istic. In  many  cases,  especially  when  the  number  of 
the  reacting  molecules  is  great,  the  experimental  re- 
sults agree  better  with  an  equation  of  reaction  corre- 
sponding to  a  lesser  number  of  reacting  molecules  than 
is  expressed  be  the  chemical  equation.  In  such  cases 
an  explanation  of  the  seemingly  abnormal  behavior 
of  the  reaction  has  been  found  by  the  supposition  that 
the  investigated  reaction  is  composed  of  two  or  more 
partial  reactions  of  which  the  slowest  one  corresponds 
to  the  equation  found  experimentally.  The  hypothesis 
made  has  in  some  cases  been  verified  experimentally. 
As  has  been  known  from  the  times  of  the  alchemists, 
temperature  has  a  very  great  influence  in  hastening 
chemical  processes.  This  was  also  stated  by  Wilhelmy, 
when  he  investigated  the  inversion  of  cane  sugar.  He 
found  that  the  velocity  of  reaction  increases  nearly 
exponentially  with  temperature.  The  same  was  stated 
by  Berthelot  for  the  formation  of  ester  from  an  alcohol 
and  an  acid,  a  reaction  which*,  being  one  of  the  first 
examined  rather  closely,  has  played  a  preponderating 
role  in  this  chapter.  The  formula,  representing  the 
velocity  k  of  reaction  is  then: 

*;*,  =  *„  10*  " 

Berthelot  has  himself  said  that  the  experiments  were 
not  sufficient  in  number  for  ascertaining  if  his  formula 
is  correct.  The  values  given  by  him  are 

Temp.  Jb(obs.)  k  (calc.)  B 

8°  0.0004  0.0004 

85°  0.074  0.0456  0.0281 

100°  0.17  0.115  0.0307 

170°  8.50  8.50  0.0243 


124  THEORIES  OF  SOLUTIONS. 

The  value  of  B  decreases  with  rising  temperature  and 
this  is  the  case  for  most  processes  studied  hitherto.  I 
therefore  in  1889  examined  the  different  determinations 
available  at  that  time  and  found  that  another  formula 
gives  good  results,  viz. : 

d  log  k      A     .      .       ,  Ti-  To  .  .      . 
~dt     =  T~2 '     s   1=        TT     +    s    ° 

where  A  is  a  constant  and  T  designates  absolute  tem- 
perature. This  formula,  as  well  as  that  of  Berthelot, 
is  a  special  case  of  one  proposed  by  van't  Hoff  and 
containing  both  the  two  terms  occurring  in  the  two 
formulas  above. 

dlogjc  _  A  •  » 
dt       =T2  +  tf- 

I  found  that  the  formula  with  only  A/ T2  corresponds 
very  well  and  hi  most  cases  better  with  the  experi- 
mental results  of  different  investigators  than  the  em- 
pirical formulae  proposed  by  these  investigators  do. 
It  has  a  theoretical  meaning  and  must  be  preferred 
to  formulae  containing  a  greater  number  of  empirical 
constants,  as  does  the  formula  of  van't  Hoff. 

Van't  Hoff  called  attention  to  a  rather  remarkable 
circumstance,  namely  that  the  increase  in  the  value 
of  k  for  10  degrees  is  in  most  cases  about  in  the  pro- 
portion 1  to  2  or  1  to  3.  But  there  are  rather  great 
exceptions;  thus  the  decomposition  of  phosphoreted 
hydrogen  PH3  into  its  elements  accelerates  very  much 
more  slowly  with  temperature,  namely  in  the  propor- 
tion 1  to  1.2  for  an  interval  of  10  degrees.  But  it  must 
here  be  remarked  that  the  observations  are  made  (by 
Kooy)  at  256  and  367°  respectively,  so  that  if  my  formula 


VELOCITY  OF  REACTION.  125 

is  accepted  the  quotient  increases  to  2.5  at  27°  C.  The 
same  remark  may  be  made  regarding  the  gas  reaction 
studied  by  Smits  and  Wolff: 

2CO  =  C02+C, 

which  according  to  the  chemical  equation  ought  to  be 
bimolecular,  as  2  molecules  of  CO  are  necessary  for  the 
reaction,  but  which  is  found  to  be  monomolecular. 
This  is  explained  by  assuming  two  consecutive  reactions 
of  which  the  first  has  a  much  smaller  velocity  than  the 

second,  namely: 

1)  CO  =  C+0, 

2)  CO+0  =  C02. 

The  velocity  of  this  reaction  is  found  to  increase 
in  the  proportion  1  to  1.42  for  10°  between  256°  and 
340.  Reduced  to  300°  abs.  (  =  27°  C.)  the  increase 
reaches  1  to  3.53  for  10°  C.  The  extreme  values  of  the 
said  proportion  amongst  the  processes  cited  by  van't 
Hoff  seem  to  be  shown  by  the  two  reactions  which 
have  been  studied  more  than  any  other,  namely  the  in- 
version of  cane  sugar  and  the  saponification  of  ethyl 
acetate  by  hydroxyl  ions  with  the  values  1  to  4.0  and  1 
to  1.77  at  27°  C.  This  latter  value  differs  rather  much 
from  that  which  holds  for  the  saponification  of  esters 
by  means  of  acids.  The  temperature  coefficient  of 
these  reactions  was  determined  by  Price.  The  propor- 
tion reduced  to  300°  absolute  and  a  10°  interval  is  about 
1  to  2.35  for  ethyl  acetate  and  does  not  differ  much  for 
the  other  esters. 

The  experiments  of  Kremann  give  about  as  high 
values  of  the  said  proportion  as  that  found  for  cane 
sugar,  namely  1  to  4.1  for  the  formation  of  C«jH6HS04 


126  THEORIES  OF  SOLUTIONS. 

in  the  absence  of  water  and  1  to  4  for  the  formation  of 
ethyl  ether  from  C2H5OH  and  C2H5HS04.  In  aqueous 
solution  the  first  proportion  sinks  to  1  to  2.5 — all 
figures  reduced  to  300°  absolute.  (The  experimental 
error  is  in  these  cases  rather  great.) 

At  low  temperatures  the  increase  goes  on  very  rapidly 
with  temperature.  Thus  Plotnikow  found  for  the  said 
proportion  at  —  90°  1  to  6.2  for  the  reaction 

C2H4  +  Br2  =  C^EUBrz. 

If  the  said  figure  is  reduced  to  300°  absolute  it  gives 
the  proportion  1  to  1.97. 

Therefore  van't  Hoff 's  rule,  stating  that  the  order  of 
magnitude  of  the  increase  of  velocities  of  reaction  in 
an  interval  of  10°  is  always  the  same  for  ordinary  re- 
actions, is  much  nearer  to  the  truth  if  all  values  are 
reduced  to  the  same  temperature,  e.  g.,  to  300°  absolute. 

We  may  express  this  rule  more  simply  in  other  words 
by  saying  that  the  constant  A  of  the  formula  above  (p. 
124)  is  of  the  same  order  of  magnitude  for  different 
reactions.  We  find  for  cane  sugar  and  ethyl  acetate 
saponified  by  bases  or  by  acids  12,820,  5,580  and 
8,700  respectively. 

There  are  some  very  remarkable  exceptions  to  van't 
Hoff  s  rule.  The  first  is  the  decay  of  radioactive  sub- 
stances, which  is  independent  of  the  temperature  so 
that  A  =  0.  The  second  is  the  solution  of  metals  in 
dilute  acids.  Ericson  Aure'n  determined  the  velocity 
of  reaction  when  zinc  dissolves  in  0.1  normal  hydro- 
chloric acid.  He  found  that  it  increased  only  3  per 
cent,  when  the  temperature  rose  from  9°  to  50°  C. 
This  increase  falls  absolutely  within  the  experimental 


VELOCITY  OF  KEACTION,  127 

errors.  In  more  concentrated  solutions  of  the  acids 
a  greater  increase  in  the  velocity  of  reaction  with 
temperature  is  observed,  according  to  the  experiments 
of  Guldberg  and  Waage.  The  velocity  of  reaction  at 
18°  compared  with  that  at  0°  in  hydrochloric  acid  was 
found  by  them  to  be 

for  1.3n.  HC1  1.58 

2   n.HCl  1.68 

2.671.  HC1  1.70 

4   n.HCl  2.44 

8   n.  HC1  3.25 

Spring  dissolved  iceland  spar  with  natural  surfaces 
of  cleavage  in  10  per  cent.  HC1  (about  3-normal)  and 
found  that  the  velocity  of  reaction  increases  to  about 
double  its  value  in  20  degrees  (at  25°  C.).  This  figure 
agrees  very  closely  with  that  found  for  the  solution  of 
zinc  in  hydrochloric  acid  of  the  same  strength.  If  the 
crystals  were  cut  with  surfaces  parallel  with  or  per- 
pendicular to  the  chief  axis  the  rate  of  increase  with 
temperature  was  higher  (about  as  1  to  3  between  15 
and  35)  but  rather  irregular. 

Recently  I  investigated  the  velocity  of  the  solution 
of  the  active  deposit  from  actinium  emanation  in  water 
and  0.001  normal  acetic  acid  at  15°  and  at  62°  and  found 
no  appreciable  difference  at  the  two  temperatures. 

The  photochemical  reactions  are  only  to  a  very 
insignificant  degree  dependent  on  the  temperature  in 
regard  to  their  velocities.  Thus  for  instance  the  ratio 
of  increase  in  an  interval  of  10°  was  found  to  be  for 
the  following  reactions  (the  table  is  taken  from  Plotni- 
kow's  Photochemistry). 

Polymerization  of  anthracene 1  to  1.21 

Oxidation  of  quinine  by  means  of  chromic  acid ...  1  to  1.06 


128  THEORIES  OF   SOLUTIONS. 

Reaction  of  chlorine  on  hydrogen 1  to  1.21 

Reaction  of  oxalic  acid  with  ferric  chloride 1  to  1.01 

Reaction  of  oxygen  on  hydriodic  acid 1  to  1.39 

Transformation  of  styrol  to  metastyrol 1  to  1.36 

Oxidation  of  dioxide  of  sulphur  with  oxygen.  .  .  .1  to  1.20 
Reaction  of  oxalic  acid  and  mercuric  chloride.  .  .1  to  1.12 
The  photographic  process  with  silver  bromide 
gelatine 1  to  1.00,  to  1  to  1.03 

The  reaction  evidently  depends  upon  the  absorption 
of  the  active  light  rays,  which  alters  very  little  with 
temperature.  Another  peculiarity  which  is  without 
doubt  connected  with  the  low  coefficient  of  temperature 
is  that  the  photochemical  processes  behave  as  if  they 
were  monomolecular.  Thus  Bodenstein  observed  that 
hydriodic  acid,  which  at  high  temperatures  is  decom- 
posed according  to  the  equation: 

2HI  =  H2  +  I2 

which  reaction  is  in  fact  found  to  follow  the  laws  valid 
for  bimolecular  reactions,  nevertheless  on  decomposi- 
tion by  means  of  light  at  low  temperature  obeys  the 
equation: 

HI  =  H  +  I, 

i.  e.j  behaves  as  a  monomolecular  reaction. 

From  this  we  conclude  that  each  molecule  of  HI 
independently  of  other  similar  molecules  is  decomposed 
by  the  light  waves.  These  tear  asunder  the  molecules 
by  the  intensity  of  their  vibrations,  whereas  at  high 
temperature  bonds  connecting  the  atoms  H  and  I  in 
the  molecule  HI  are  weakened,  so  that  a  dissociation 
takes  place  at  first  after  the  impact  of  another  molecule 
of  HI,  when  there  is  an  opportunity  for  the  atoms  H 
and  I  to  combine  with  another  atom  of  H  or  I  respec- 
tively. 


VELOCITY  OF  KEACTION.  129 

Another  exception  to  the  rule  of  van't  Hoff  is  found 
in  the  spontaneous  decomposition  of  certain  enzymes  or 
similar  substances  such  as  hsemolysins.  These  latter 
are  subject  to  an  exceedingly  high  influence  of  tem- 
perature. Thus  for  instance  Madsen  and  Famulener 
found  for  a  hsemolysin  contained  in  blood  serum  from 
a  goat  a  value  of  A  =  99,200,  corresponding  to  an  in- 
crease in  the  velocity  of  reaction  in  the  proportion  1  to 
2.6  per  degree  at  50°.*  A  little  less  was  the  influence 
of  temperature  on  the  destruction  of  tetanolysin  and 
vdbriolysin,  A  being  81,000  and  64,000  respectively. 
The  destruction  of  2  per  cent,  solutions  of  rennet,  pepsin, 
invertase  and  trypsin  also  possess  very  high  values  of 
A,  namely  45,000,  38,000,  36,000  and  31,000  respec- 
tively, corresponding  to  a  doubling  of  the  effect  in  a 
rise  of  the  temperature  of  1.5,  2,  2.1  and  2.4  degrees  at 
about  60°. 

On  the  other  hand  the  reactions  of  these  substances 
with  other  substances  usually  agree  approximately 
with  the  saponification  of  ethyl  acetate  by  means  of 
bases  in  regard  to  then*  hastening  by  temperature. 
Sometimes  they  give  rather  low  values  of  A,  for  instance 
the  inversion  of  cane  sugar  by  means  of  invertase  has  a 
value  of  A  =  4,500  between  20°  and  30°,  5,500  between 
0°  and  20°  (Euler  and  Beth  af  Ugglas)  and  the  precipi- 
tation of  egg-white  by  means  of  precipitin  only  3,150. 

It  is  well  worth  noting  that  different  vital  processes 
such  as  the  assimilation  hi  plants,  the  respiration  of 
plants,  the  cell  division  in  eggs  possess  nearly  the  same 

*  This  circumstance  may,  as  Madsen  remarks,  be  of  use  for  the  human 
body.    After  the  toxin  has  entered  the  blood,  the  temperature  rises 
sometimes  2-3  degrees — fever  temperature — and  the  poison  is  destroyed 
about  10  times  more  rapidly  than  without  the  fever-heat. 
10 


130  THEORIES  OF  SOLUTIONS. 

value  of  A  (between  6,000  and  8,000)  corresponding  to 
an  increase  in  the  proportion  of  about  1  to  2  for  a  rise 
of  temperature  of  10°  C. 

Regarding  these  enzymatic  and  life-processes  the 
literature  is  collected  in  Immunochemistry  by  S. 
Arrhenius. 


LECTURE  VIII. 

CONDUCTIVITY    OF    SOLUTIONS    OF    STRONG 
ELECTROLYTES. 

As  we  have  seen  above,  Kirchhoff  as  early  as  1858 
applied  thermodynamics  to  equilibria  in  solutions. 
From  the  change  of  solubility  with  temperature  he 
calculated  the  heat  evolved  at  solution  according  to 
the  equation  of  Clapeyron.  Thus  he  found  for  one 
gram  of  ammonia  gas  at  20°  214  cal.  and  for  one  gram 
of  sulphur  dioxide  at  20°  97.7  cal.,  using  Bunsen's 
figures  for  the  solubility  of  these  gases.  These  calcu- 
lated heats  do  not  agree  very  well  with  those  deter- 
mined calorimetrically  by  Julius  Thomsen,  namely  494 
cal.  for  1  g.  NH3  and  120  cal.  for  1  g.  S02.  Kirchhoff 
demonstrated  that  analogous  considerations  of  the 
vapor  tension  of  salt  solutions  lead  to  determination 
of  the  heat  of  solution  of  the  salt  and  the  heat  of 
dilution  of  its  solutions.  Regarding  this  latter  point 
he  showed  that  the  experimental  evidence,  that  at  high 
dilutions  of  salts  a  further  addition  of  water  has  no 
thermal  effect,  leads  to  the  conclusion  that  the  relative 
lowering  of  the  vapor  tension  of  salt  solutions  does 
not  change  with  temperature,  which  rule  had  been 
demonstrated  experimentally  by  von  Babo. 

This  work  was  continued  by  Guldberg  in  1870  and  by 
van't  Hoff  (1885)  who  introduced  his  law  on  the  analogy 
of  solution  and  evaporation. 

These  deductions  concern  the  heterogeneous  equilib- 

131 


132  THEORIES  OF  SOLUTIONS. 

rium  between  a  gas  or  a  solid  substance  in  equilibrium 
with  its  solution.  Much  more  important  are  the  homo- 
geneous equilibria.  Horstmann  had  deduced  the  laws 
of  these  for  the  gaseous  state  and  these  are  of  course 
according  to  van't  Hoffs  law  applicable  also  to  di- 
lute solutions. 

Berthelot  and  Pean  de  S.  Gilles  had  in  1862-1863 
investigated  the  equilibrium  between  an  alcohol,  an 
organic  acid  and  their  products  of  reaction,  water  and 
ether.  The  reaction  was  allowed  to  take  place  either 
hi  a  gaseous  mixture  or  in  a  liquid,  to  which  was  in  some 
cases  added  benzene  or  acetone.  The  results  of  this 
classical  investigation  regarding  a  homogeneous  equilib- 
rium were  calculated  in  1877  by  van't  Hoff  and  in  1879 
independently  by  Guldberg  and  Waage.  They  found 
that  for  the  combination  of  1  molecule  of  ethyl  alcohol 
with  n  molecules  of  acetic  acid  and  m  molecules  of 
water,  the  following  equation  holds  good: 

(m  +  x)x  =  4(1  —  x)(n  —  x)} 

where  x  is  the  number  of  alcohol  and  acid  molecules 
transformed  into  x  molecules  of  ethyl  acetate.  This  is 
exactly  the  form  of  equation  which  holds  for  the  gaseous 
state  and  according  to  van't  Hoff's  law  also  for  the  dis- 
solved state.  Another  example  was  the  determination 
of  the  dissociation  of  nitrogen  peroxide  N204  into  2NO2. 
This  equilibrium  takes  place  as  well  in  the  gaseous  as 
hi  the  liquid  state,  in  the  latter  case  diluted  with  some 
organic  solvent,  such  as  chloroform.  In  such  experi- 
ments of  Cundall  (1891)  the  rate  of  dissociation  was 
determined  colorimetrically.  The  experiments  agree 
very  well  with  the  gas  laws,  as  Ostwald  proved  a  little 
later. 


CONDUCTIVITY  OF  STRONG  ELECTROLYTES.        133 

These  applications  of  the  theoretical  laws  were  rather 
few,  until  Ostwald  in  1888  demonstrated  the  applica- 
bility of  Guldberg  and  Waage's  law  of  equilibrium  hi 
the  electrolytic  dissociation  of  weak  acids,  which  work 
was  completed  some  years  later  by  Bredig's  work  on 
the  weak  bases.  The  experimental  material  regarding 
more  than  200  weak  acids  and  more  than  40  bases  was 
absolutely  unrivalled  and  the  evidence  of  the  dissocia- 
tion theory  was  generally  regarded  as  indubitable. 
But  on  the  other  hand  we  remember  that  Planck  had 
at  the  same  time  as  Ostwald  tried  to  apply  the  gas 
laws  to  the  electrolytic  dissociation  of  salts  without 
success.  The  same  may  be  said  regarding  the  strong 
acids  and  bases.  For  all  these  so-called  strong  elec- 
trolytes van't  Hoff  gave  an  empirical  formula,  namely: 


a  is  the  degree  of  dissociation  and  v  is  the  volume  hi 
which  one  gram-molecule  of  the  strong  electrolyte  is 
dissolved,  K  is  a  constant.  Instead  of  the  exponent  2, 
which  is  demanded  by  theory,  van't  Hoff  introduced 
the  exponent  1.5  which  accords  much  better  with  the 
experiments  in  these  cases.  As  there  now  exists  a 
much  greater  number  of  electrolytes  belonging  to  this 
class,  than  to  that  which  obeys  the  gas  laws,  it  has  been 
rightly  said  that  this  deviation  from  the  gas  laws  is 
really  the  weak  point  in  the  electrolytic  dissociation 
theory.  But  for  just  this  case  by  the  help  of  a  great 
number  of  rather  simple  empirical  rules  we  are  able 
to  calculate  the  equilibria  for  these  substances  with  a 
great  degree  of  accuracy.  As  these  play  a  very  im- 
portant role  in  nature,  as  well  in  the  waters  of  the 


134  THEORIES  OF  SOLUTIONS. 

sources,  rivers,  seas  and  oceans,  as  in  the  humors  of 
the  animal  bodies  or  of  the  plants,  I  will  enter  a  little 
closer  upon  this  chapter. 

The  calculation  of  the  dissociated  part  is  performed 
very  simply  by  taking  the  quotient  of  the  molecular 
conductivity  of  the  solution  hi  question  and  that  of  the 
same  electrolyte  in  infinite  dilution,  i.  e.,  the  limit  value 
to  which  the  molecular  conductivity  tends  with  increas- 
ing dilution.  This  limit  value  may  be  written  as  the 
sum  of  two  components,  the  one  valid  for  the  anion  and 
the  other  for  the  cation.  These  values  are  determined 
by  means  of  the  migration  numbers  first  determined  by 
Hittorf  and  later  unproved  by  different  investigators. 
They  have  at  18°  the  following  values  (according  to 
Kohlrausch).  K  64.6,  NH4  64.2,  Na  43.5,  Li  33.4, 
Ag  54.3,  Rb  67.5,  Cs  68,  Tl  66.0,  H  315,  HBa  55.5, 
y2Mg  46.0,  HZn  46.7,  J^Pb  61.3,  F  46.6,  Cl  65.5, 
Br  67.0, 1  66.5,  N03  61.7,  C103  55.0,  COOH  45,  CH3C02 
33.7,  OH  174,  HSO*  68.4,  SCN  56.6. 

For  organic  ions  Ostwald  and  Bredig  have  given  a 
great  number  of  measurements,  which  indicate  that 
the  conductivity  generally  decreases  with  the  increasing 
number  of  atoms  contained  in  the  ion. 

The  conductivity  of  the  different  ions  depends  on  the 
solvent  and  its  temperature.  An  increase  of  the  tem- 
perature augments  the  conductivity,  so  that  that  of 
the  less  conducting  ion  increases  in  a  higher  propor- 
tion than  that  of  the  better  conducting  one,  i.  e.,  the 
different  conductivities  approach  each  other  with  in- 
creasing temperature  as  is  seen  from  the  following 
figures  calculated  from  the  experiments  of  Noyes  and  his 
pupils: 


CONDUCTIVITY  OF  STRONG  ELECTROLYTES.        135 

Ion             Temp.             18  100  156  218  281  306°  C. 

K 64.6  206.5  312  412  502  560 

Na 43.5  154.5  242  347  467  520 

NH* 65.2  207.5  315  428  

Ag 52.3  183.5  295  402  501  549 

^Ba 53.4  201.5  325  462  656  784 

^Mg 55.9  177.5  287  427  

H 313.5  642.5  772  852  877  864 

Cl 65.5  207.5  313  413  503  560 

H2P04 24.5   87.5  158  

NO3 63.5  183.5  275  378  464  516 

HSO« 58.2  248.5  403  653  958  1165 

CH3C02 34.6  130.5  208  313  413  474 

OH 173  339.5  593  713  —  — 

These  figures  are  very  instructive.  The  ion  Ag 
which  at  18°  C.  has  six  tunes  less  conductivity  than 
the  H-ion  reaches  nearly  64  per  cent,  of  the  conductivity 
of  H  at  306°.  The  acetate  ion  CH3C02  has  five  times 
smaller  conductivity  than  the  ion  OH  at  18°  but  reaches 
about  44  per  cent,  of  it  at  218°.  Also  minor  differences 
as  between  K  and  Na  diminish  at  higher  temperatures 
as  well  as  the  proportion  between  the  conductivities 
of  chlorine  or  N03  and  CHsCC^.  An  exception  to  this 
rule  is  found  for  the  bivalent  ions,  which  probably  tend 
to  reach  double  the  value  of  that  for  monovalent  ions, 
with  increasing  temperature.  HS04  has  already 
reached  this  value  at  306°,  but  the  barium  ion  has 
at  306°  only  attained  a  value  about  50  per  cent,  higher 
than  that  of  the  monovalent  ions. 

A  peculiar  property  is  that  the  dissociation  diminishes 
with  increased  temperature,  which  is  also  true  for  most 
weak  acids.  The  non-dissociated  part  (1  —  a)  follows 
a  rule  enunciated  by  Ostwald,  namely  that  in  not  too 
concentrated  solutions  of  equivalent  strength  it  is 
proportional  to  the  product  v&i  of  the  valencies  Vi  and 


136  THEORIES  OF  SOLUTIONS. 

vz  of  the  two  ions.     Noyes  gives  the  following  instruc- 
tive table  of  (I—a)  expressed  in  per  cent.: 

Type  Eq.  per  Lit.  18°  100°  156° 

Obs.      Calc.       Obs.      Calc.       Obs.      Calc. 


KC1* 

0.04 

12 

12 

15 

15 

17 

17 

KC1 

0.08 

15 

14 

18 

17 

21 

20 

BaCl2,  KjSOi 

0.08 

28 

28 

34 

34 

40 

40 

MgS04 

0.08 

55 

56 

68 

68 

81 

80 

Type 

Eq.  per  Lit. 

218° 

281«> 

306° 

Obs. 

Calc. 

Obs. 

Calc. 

Obs.      < 

:ak 

KC1* 

0.04 

20 

20 

25 

25 

31 

31 

KC1 

0.08 

25 

24 

31 

32 

39 

38 

Bad,,  K,S04 

0.08 

51 

48 

65 

64 

74 

76 

MgS04 

0.08 

93 

96 

— 

— 

— 

— 

The  exponent  in  the  equilibrium  formula,  which  by 
van't  Hoff  has  been  calculated  to  1.5  was  according 
to  Noyes'  experiments  variable  between  1.4  and  1.5 
with  an  average  value  of  1.46.  With  the  aid  of  this 
formula  of  the  equilibrium  it  is  possible  to  calculate  the 
degree  of  dissociation  at  any  concentration. 

Noyes  also  stated  a  rule  found  by  myself,  namely, 
that  the  dissociation  of  each  of  two  salts  with  a  common 
ion  hi  a  mixture  is  just  as  great  as  the  dissociation  of 
each  salt  itself  would  be,  if  the  concentration  of  the 
common  ion  were  the  same  as  in  the  mixture  (the  rule 
of  isohydric  solutions).  An  analogous  rule  may  be 
used  for  a  mixture  of  any  number  of  salts.  This  rule 
has  a  higher  degree  of  exactness  than  those  given  above. 

With  the  aid  of  these  simple  rules  it  is  possible  to 
calculate  the  degree  of  dissociation  for  salts  in  general. 
Very  significant  is  the  rule  that  the  exponent  in  the 
equilibrium  formula  is  the  same  for  all  salts,  inde- 
pendently of  the  number  of  ions  into  which  they  decom- 
pose. 

*  For  the  strong  monovalent  acids,  HC1  and  HNOs,  and  for  the  bases, 
NaOH  and  Ba(OH)2,  the  quantity  (1 — a)  is  only  about  half  as  great  as 
for  the  salts  of  the  same  type. 


CONDUCTIVITY  OF  STRONG  ELECTROLYTES.       137 

The  conductivity  of  the  ions  depends  also  in  a  high 
degree  on  the  solvent  medium.  Thus  for  instance  the 
conductivities  at  18°  in  0,  50,  80  and  100  p.  c.  solutions 
of  alcohol  are  the  following: 


Per  Cent  Alcohol.     K 

Na 

NH4 

H 

OH 

0 

65.3 

44.4 

64.2 

318 

174.9 

50 

21.8 

17.0 



95.8 

— 

80 

18.4 

14.0 

17.9 

50.2 

26.1 

100 

21.5 

14.5 

20 

32.1 

16.5 

Cl 

(C,H.),NH, 

Salicylat. 

Acetate. 

CHaCNCOO 

I 

65.9 

36.1 

32 

38.3 

36.5 

66.7 

23.2 



12.0 



14.0 

22.6 

17.1 

12.2 

11.3 

12.2 

14.0 

19.1 

23.8 

12.6 

12.6 

12.4 

15.0 

27.5 

Most  of  these  determinations  were  made  by  Godlewski, 
that  regarding  OH  by  Hagglund. 

All  the  ions,  except  H  and  OH,  possess  a  minimum 
of  conductivity  at  a  certain  concentration  of  the  alcohol. 
This  minimum  is  found  at  different  percentages  of 
alcohol;  for  Cl,  I,  K  and  Na  at  about  85  per  cent.,  for 
the  salicylate  ion  at  about  75  per  cent,  and  for  the 
cyanacetate  ion  at  about  70  per  cent.  Probably  this 
minimum  depends  upon  the  decrease  of  the  fluidity 
with  decreasing  strength  of  the  alcohol  until  it  reaches 
40  per  cent.,  where  the  fluidity  has  its  minimum  at  18°. 
Evidently  the  minimum  of  conductivity  does  not 
coincide  with  that  of  the  fluidity,  but  there  is  another 
factor  which  has  a  still  greater  influence. 

The  figures  for  H  and  OH  hi  pure  alcohol  are  very 
interesting,  their  conductivities  being  of  the  same  order 
of  magnitude  as  that  of  other  ions.  The  hydrogen 
ion  has  also  in  alcohol  the  greatest  conductivity,  but 
is  not  very  much  superior  to  iodine  and  chlorine;  one 
might  expect  this  position  of  the  hydrogen  according  to 


138 


THEORIES  OF  SOLUTIONS. 


its  low  atomic  weight.  The  hydroxyl-ion  falls  far 
below  all  the  ions  consisting  of  simple  atoms  and  also, 
curiously  enough,  below  NH4.  This  circumstance,  as 
well  as  the  strong  increase  in  the  conductivity  of  the 
H-  and  OH-ion  with  the  addition  of  small  quantities 
of  water,  in  spite  of  the  increased  viscosity,  indicates 
that  the  exceptionally  great  conductivity  of  these  two 
ions  hi  water  is  probably  due  only  to  the  fact  that  they 
are  the  two  ions  into  which  water  is  electrolytically 
decomposed. 

According  to  Godlewski's  figures  the  conductivities 
of  Na,  K  and  Cl  in  alcoholic  solutions  containing  from 
0  to  100  per  cent,  alcohol  are  the  following  at  18°  C. : 


Per  Cent. 
Alcohol. 


Cl 


Na 


Mean. 


H  H 

Obs.       Red. 


OH    Fluidity. 
Bed. 


0 

1 

1 

1 

1 

318 

318 

174.9 

1 

10 

0.766 

0.781 

0.766 

0.771 

234.6 

307 

— 

0.689 

20 

0.583 

0.605 

0.559 

0.582 

188.7 

324 

— 

0.476 

30 

0.473 

0.516 

0.449 

0.479 

147.7 

308 

— 

0.381 

40 

0.401 

0.427 

0.361 

0.396 

120.1 

303 

— 

0.348 

60 

0.354 

0.379 

0.334 

0.356 

95.8 

269 

— 

0.354 

60 

0.307 

0.339 

0.303 

0.316 

75.9 

240 

— 

0.375 

70 

0.275 

0.317 

0.299 

0.297 

62.2 

209 

— 

0.431 

80 

0.261 

0.312 

0.282 

0.285 

50.2 

176 

91.6 

0.510 

90 

0.261 

0.307 

0.288 

0.285 

40.6 

143 

— 

0.625 

100 

0.363 

0.324 

0.329 

0.339 

32.1 

95 

48.7 

0.831 

The  conductivity  of  the  three  monovalent  salt  ions 
sinks  at  first  rapidly,  reaches  50  per  cent,  at  about  28  per 
cent,  alcohol,  33.3  at  about  56  per  cent.,  then  sinks  slowly 
to  a  minimum  of  about  28  per  cent,  at  85  per  cent,  alco- 
hol and  then  rises  again  to  about  34  per  cent,  at  100  per 
cent,  alcohol.  If  we  correct  the  values  of  Godlewski  for 
H  tabulated  under  H  obs.  by  dividing  them  by  the  mean 
values  giving  the  conductivity  of  monovalent  mono- 
atomic  salt  ions,  we  might  expect  to  find  a  constant  value 


CONDUCTIVITY  OF  STRONG  ELECTROLYTES.        139 

if  the  influence  of  alcohol  were  the  same  on  the  H-ion 
as  on  K,  Na  and  Cl,  but,  instead  of  that  we  get  the 
figures  under  H  red.  These  last  figures  remain  nearly 
constant  until  40  per  cent,  of  alcohol  are  added — they 
decrease  slowly,  but  only  to  the  extent  of  5  per  cent, 
and  thereafter  they  sink  with  a  mean  value  of  32  units 
(10  per  cent.)  for  each  step  of  10  per  cent,  of  alcohol 
added  until  90  per  cent,  of  alcohol  is  reached.  There- 
after for  the  last  10  per  cent,  of  alcohol  the  decrease  is 
not  less  than  48  units  (15  per  cent.).  The  few  figures 
for  OH,  treated  in  the  same  manner,  give  a  decrease 
between  80  and  100  per  cent,  of  alcohol,  which  is  nearly 
in  the  same  proportions  as  the  corresponding  decrease 
for  the  figures  under  H  red. 

This  observation  may  be  explained  in  the  following 
manner.  The  wandering  of  the  ions  is  hampered  by 
their  collision  with  molecules  (of  water  or  alcohol). 
The  ions  H  and  OH  behave  exceptionally  in  water 
because  when,  for  instance,  an  H-ion  hits  a  water 
molecule  HOH  on  its  OH-side  it  may  unite  with  the  OH 
and  set  the  H-ion  of  the  water  molecule  free  so  that  it 
may  continue  to  carry  away  positive  electricity.  It  is 
just  as  in  the  Grotthuss'  chain,  except  that  it  is  not 
necessary  that  the  molecules  turn  around.  If  another 
ion  than  H  or  OH  hits  the  water  molecule,  the  effect 
of  an  exchange  with  the  H  or  OH  in  a  water  molecule 
would  be  the  same  as  a  decomposition  of  the  water  into 
H-  and  OH-ions,  which  would  be  accompanied  by  a  rise 
of  the  free  energy,  which  is  impossible.  As  the  alcohol 
acts  as  an  entremely  weak  acid,  i.  e.,  may  give  the  ions 
H  and  C2H50,  perhaps  the  high  conductivity  of  H  in 
alcohol  may  be  partly  explained  by  this  circumstance, 


140  THEORIES  OF  SOLUTIONS. 

but  in  all  cases  its  superiority  over  other  ions  is  so 
small  that  the  ability  of  the  alcohol-molecules  to 
separate  into  their  ions  must  be  regarded  as  rather 
insignificant  compared  with  that  of  the  water  molecules. 
For  the  sake  of  comparison  I  have  added  to  the  above 
table  the  figures  of  the  relative  fluidity  of  alcoholic  solu- 
tions. It  has  long  been  maintained  that  the  conduc- 
tivity is  proportional  to  the  fluidity.  The  change  of 
both  with  temperature  for  weak  salt  solutions  is  very 
nearly  the  same,  the  fluidity  increasing  by  about  2.4 
per  cent,  per  °  C.  at  20°,  which  is  very  nearly  the 
average  temperature  coefficient  of  the  conductivity  of 
dilute  salt-solutions.  Therefore  G.  Wiedemann,  Bouty 
and  F.  Kohlrausch  were  inclined  to  regard  these  two 
temperature  coefficients  as  identical  and  to  maintain 
that  the  increase  of  the  conductivity  is  due  to  the 
increase  of  the  fluidity,  which  was  further  explained  by 
the  supposition  that  the  ions  were  covered  with  a  layer 
of  water  molecules  and  that  this  complex  moved  in 
the  water.  The  main  difficulty  with  this  hypothesis 
was  that  the  conductivity  of  acids  and  of  bases  increases 
much  less,  about  1.6  and  2.0  per  cent,  per  °  C.  from 
18  °  C.  on,  respectively.  The  increase  in  the  conduc- 
tivity is  here  less  than  that  of  the  fluidity.  The  same 
is  valid  for  the  salts.  According  to  Noyes  the  values 
of  the  conductivity  and  that  of  the  fluidity  are  at  the 
temperatures  18°,  100°  and  156°  the  following,  if  that 
at  18°  is  taken  as  unity. 

A  at  18°  18°  100°  156° 

Fluidity  (p 1.000  3.717  5.894 

HC1 379  1.000  2.243  2.863 

NaOH 216.5  1.000  2.743  3.856 

Ba(OH)2 222  1.000  2.905  3815 


CONDUCTIVITY  OF  STRONG  ELECTROLYTES.        141 

A  at  18°  18°  100°  156° 

KC1 130.1  1.000  3.183  4.805 

NaCl 109.0  1.000  3.322  5.092 

AgN03 115.8  1.000  3.168  4.921 

NaCH3C02 78.1  1.000  3.648  5.761 

BaN2O6 116.9  1.000  3.294  5.133 

K2SO4 132.8  1.000  3.426  5.388 

As  is  seen  from  these  figures  the  fluidity  increases 
more  rapidly  than  the  molecular  conductivity  A  of 
extremely  attenuated  solutions,  which  are  considered 
here. 

This  behavior  seems  to  be  general,  as  soon  as  the 
solvent  is  not  too  much  changed.  The  trivalent  La-ion 
forms  an  exception  according  to  Johnston,  the  quotient 
A//  increasing  from  640  to  675  in  the  interval,  18°  to 
156°.  The  same  is  the  case  for  bivalent  ions  as  J/£Ba 
and  ^S04  as  is  seen  from  the  figures  by  Noyes  given 
above.  Also  in  the  table  above  for  small  additions  of 
alcohol  (not  exceeding  40  per  cent.),  the  fluidity  de- 
creases much  more  than  the  conductivity  of  the  ions 
Cl,  Na  and  K.  I  have  proved  the  same  to  be  valid 
for  small  additions  of  different  organic  substances  to 
water.  The  different  electrolytes  are  not  influenced  in 
the  same  degree  and  therefore  I  have  divided  them  in 
four  groups:  (1)  strong  acids  and  bases,  (2)  salts  of 
two  monovalent  ions,  type  KC1,  (3)  salts  of  monovalent 
cations  with  divalent  anions,  type  K2S04,  (4)  salts  of 
divalent  cations  with  monovalent  anions,  type  BaCl2. 
The  experimental  results  are  given  in  the  following 
table  in  which  (A  —  1)  gives  the  increase  of  the  viscosity 
and  a  the  increase  of  resistance  in  per  mille  at  25°  on 
exchange  of  water  to  the  quantity  of  1  volume  per  cent, 
of  the  solution  for  the  following  substances,  so  that  the 
volume  remains  the  same. 


142  THEORIES  OF  SOLUTIONS. 

Fluidity,     lit  Group.    2nd  Group.     3rd  Group.    4th  Group 

Acetone 19  15.6  16.2  19.0  16.7 

Methyl  alcohol 21  16.2  17.5  19.2  18.0 

Ethyl  ether 26  16.3  19.9  21.4  20.9 

Allyl  alcohol 26  18.8  21.2  21.1 

Ethyl  alcohol 30  18.8  23.4  25.1  23.9 

n-Butyl  alcohol 30  18.4  22.6  27.9  24.1 

Isoamyl  alcohol 31  17.2  21.6  27.3  26.7 

n-Propyl  alcohol  ...32  19.5  27.8  27.0 

Isobutyl  alcohol....  33  19.5  24.4  28.0  26.5 

Glycerol 33  20.5  22.7  26.0  25.0 

Isopropyl  alcohol...  36  20.3  25.6  27.7  26.9 

Dextrose 40  22.9  —  — 

Galactose 40  23.2  —  —  — 

Mannite 43  25.0  — 

Cane  sugar 46  24.4  29.9  33.4  30.9 

With  weak  acids  or  bases  and  slightly  dissociated 
salts,  such  as  sulphates  of  divalent  metals,  etc.,  the  dis- 
sociation is  perceptibly  diminished  by  even  very  small 
additions  of  organic  substances.  Then  it  happens  that 
the  conductivity  changes  in  a  higher  degree  than  the 
fluidity. 

Walden,  on  the  other  hand,  investigated  the  molecular 
conductivity  of  extremely  dilute  solutions  of  tetraethyl- 
ammonium  iodide  for  26  different  solvents  and  found 
that  it  was  proportional  within  5  per  cent,  to  the 
fluidity,  as  is  indicated  by  the  following  table  (valid  for 
25°  C.). 

ij  A  AT; 

Acetone 0.00316  225  0.711 

Acetonitrile 0.00346  200  0.692 

Acetylchloride 0.00387  172  0.666 

Propionitrile 0.00413  165  0.682 

Ethyl  nitrate 0.00497  138  0.686 

Methyl  alcohol 0.00580  124       '    0.719 

Nitromethane 0.00619  120  0.743 

Methyl  rhodanide 0.00719  96  0.690 

Ethyl  rhodanide 0.00775  84.5  0.655 

Acetyl  acetone 0.00780  82  0.640 


CONDUCTIVITY  OF  STBONG  ELECTROLYTES.        143 


Acetic  acid  anhydride  .......  0.00860  76  0.654 

Epichlorhydrine  ............  0.0103  66.8  0.688 

Ethyl  alcohol  ..............  0.0108  60  0.648 

Benzonitrile  ................  0.0125  56.5  0.706 

Furfurol  ...................  0.0149  50  0.745 

Diethyl  sulphate  ............  0.0160  43  0.688 

Dimethyl  sulphate  ..........  0.0176  43  0.757 

Nitrobenzol  ................  0.0182  40  0.728 

Benzyl  cyanide  .............  0.0193  36  0.695 

Asymmetric  ethyl  sulphite  .  .  .0.0238  26.4  0.628 

Ethylcyanacetate  ..........  0.0250  28.2  0.705 

Salicylaldehyde  ............  0.0281  25  0.703 

Fonnamide  ................  0.0321     ca.  25  0.802 

Anhydride  of  citraconic  acid  .0.0338  22.5  0.760 

Anisaldehyde  ...............  0.0422  16.5  0.696 

(Glycol  .....................  0.1679  ca.  8  1.32) 

(Water  .....................  0.00891  112.5  1.00) 

This  value  is  not  valid  for  the  monovalent  ions 
Cl,  Na  and  K  in  ethyl  alcohol  at  18°;  the  product  \ij  in 
this  case  is  only  0.407  instead  of  0.648.  rj  is  the  vis- 
cosity, i.  e.,  the  inverse  value  of  the  fluidity.  Hence 
the  limit  values  of  the  conductivities  of  extremely 
diluted  solutions  are  not  in  a  constant  proportion,  as 
has  also  been  stated  by  Dutoit  and  Rappeport.  In  the 
table  regarding  the  conductivities  of  ions  the  propor- 
tion between  this  magnitude  in  alcoholic  and  in  aqueous 
solution  is:  for  OH  0.094,  H  0.101,  NH4  0.312,  Ace- 
tation  0.324,  Na  0.324,  K  0.329,  (C2H5)2NH  0.352, 
Cl  0.363,  Salicylation  0.394,  Cyanacetation  0.411, 
I  0.412  (Cf.  p.  137). 

It  must  be  remarked  that  these  figures  are  not  in 
good  agreement  with  those  given  by  Dutoit  and  Rapp- 
eport. The  discrepancies  may  serve  as  a  proof  of 
the  difficulty  of  the  measurements  in  non-aqueous 
solutions.  The  ions  OH  and  H  behave  quite  excep- 
tionally, and  OH  in  a  higher  degree  than  H  which 


144  THEORIES  OF  SOLUTIONS. 

may  perhaps,  as  stated,  be  explained  as  due  to  a  weak 
electrolytic  dissociation  of  the  alcohol  molecules  into 
H  and  C2H50. 

Dutoit  and  Duperthuis  investigated  the  relation 
between  fluidity  and  conductivity  of  Nal  in  different 
solvents  at  different  temperatures.  They  found  the 
following  values  of  the  limit  value  M.  at  0°  and  the 
values  of  17/1.  at  0°  and  at  60°,  where  77  is  the  viscosity : 

Ethyl        Propyl   Isobutyl  Isoamyl     Pyri-          Ace- 
Alcohol.     Alcohol.  Alcohol.  Alcohol,     dine.  tone. 

p*  at    0°     27.95      11.85      5.48      4.49      42.10        12.75 
17^  at    0°       0.495      0.453    0.441     0.374      0.573        0.502 
Woo  at  60°       0.457      0.443    0.397    0.269      0.562        0.517  (at  40°) 

In  all  cases  observed,  except  for  acetone,  ^  sinks 
with  increasing  temperature,  which  indicates  that 
the  conductivity  changes  less  with  temperature  than 
the  fluidity,  just  as  for  water,  according  to  Noyes, 
and  as  for  small  additions  of  organic  substances  to 
water. 

Schmidt  and  Jones  found  77^  for  KI  to  be  (at  18°) 
0.72  in  methyl  alcohol,  1.32  in  glycol  and  2.10  in  gly- 
cerol,  which  is  the  order  of  17  in  the  three  cases.  Con- 
sequently the  viscosity  or  the  fluidity  changes  in  a 
higher  proportion  than  the  conductivity. 

Quite  recently  Walden  has  investigated  the  conduc- 
tivity of  salt  solutions  in  different  organic  solvents 
at  rather  great  intervals  of  temperature.  He  found 
that  the  conductivity  can  not  be  expressed  as  a  linear 
function  of  temperature,  as  is  done  in  most  cases. 
The  curve,  which  gives  the  conductivity  as  a  function 
of  the  temperature  as  abscissa  approaches  the  abscissa 
axis  asymptotically,  when  the  temperature  sinks 
down  towards  the  absolute  zero.  The  same  is  true 


CONDUCTIVITY  OF  STRONG  ELECTROLYTES.       145 

also  for  the  fluidity.  The  extrapolation  formula  which 
leads  to  a  value  zero  as  well  for  the  conductivity  as  for 
the  fluidity  at  a  temperature  above  absolute  zero,  and 
which  has  for  instance  been  used  by  Kohlrausch  for 
determining  this  temperature  for  aqueous  solutions  to 
about  —30°,  fails  absolutely  at  low  temperatures. 
This  had  also  been  found  for  aqueous  solutions  of 
H2S04,  CaCl2  and  NaOH  by  T.  Kunz  in  1902. 

Green  and  Martin  and  Masson  investigated  the 
conductivity  /ztt  of  HC1,  KC1  or  LiCl  in  water  with 
the  addition  of  cane  sugar,  so  that  the  fluidity  (/) 
changed  in  about  the  proportion  1  to  23.  They  found 
that  a  formula  /*„  =  &/",  where  &  is  a  constant,  gives 
good  results,  n  is  found  to  be  0.5  for  HC1  and  0.7  for  KC1 
or  for  LiCl.  In  other  words  the  conductivity  changes 
much  more  slowly  than  the  fluidity,  especially  for  the 
acid,  which  agrees  wholly  with  the  behavior  of  aqueous 
solutions,  when  the  fluidity  changes  with  temperature. 

Similar  experiments  have  been  made  by  Pissarshewski 
and  Schapowalenko  on  solutions  of  KAgC2N2  and 
KBr  in  methyl  or  ethyl  alcohol,  mixed  with  different 
quantities  of  glycerol.  The  /*„,  increases  at  25°  about 
in  the  proportion  of  1:400  and  1:200  respectively  if 
the  solvent  changes  from  pure  glycerol  to  pure  methyl 
and  ethyl  alcohol  respectively,  whereas  w^  instead  of 
being  constant  simultaneously  decreases  in  the  pro- 
portion 3.5:1  and  3.7:1  respectively.  This  corresponds 
to  a  value  of  n  —  about  0.8  and  0.75.  At  45°  the  value 
of  n  increases  by  about  0.05. 

A  similar  rule  seems  to  hold  also  for  fused  electro- 
lytes according  to  Goodwin  and  Mailey.  They  examined 
nitrates   of   lithium,   sodium,   potassium,   and   silver 
11 


146          THEORIES  OF  SOLUTIONS. 

at  temperatures  up  to  500°.  The  conductivity  is 
not  strictly  proportional  to  the  temperature,  but 
increases  less  and  less  rapidly  as  the  temperature  rises. 
The  product  rj\  at  different  temperatures  is  nearly 
constant  for  KN03,  K2Cr207  and  mixtures  of  KC1  and 
NaCl,  but  decreases  (just  as  for  aqueous  solutions) 
with  rising  temperature  by  10  per  cent,  for  LiN03 
between  250  and  300°,  by  4.2  per  cent,  for  AgN03 
between  250  and  350°  and  by  6.4  per  cent,  for  NaN03 
between  350  and  450°. 

The  conductivities  of  fused  salts  have  also  been 
measured  by  Arndt  and  Gessler,  from  whom  the  follow- 
ing table  with  some  slight  extrapolations  indicated  by 
brackets  is  reproduced.  The  conductivity  is  given  in 
reciprocal  ohms  per  cm.  length  and  cm.2  cross-section. 

Temp°C 500  600  700  800  900  1000  1100 

CaCl2 1.90  2.32  2.66  (2.86) 

KC1 2.19  2.40  2.61         

KBr (1.55)  1.75  1.95  (2.15)       

KI 1.39  1.64          

Nal 2.56  2.70  2.83  (2.97)       

AgCl 4.20  4.48  4.76  4.98  5.14                         

AgBr 3.02  3.18  3.34  3.50  3.68           

Agl (2.40)  2.52  2.64  2.72  —        

NaPOs 0.30  0.55  0.80  1.05  1.30  1.54 

B2OS 7.10-e  21.10-'  46.1Q-«      

NaCl 3.34  3.66  (3.98) 

SrCl2 —  —  1.98  2.29  2.57 

The  conductivity  increases  very  regularly  and  rather 
slowly  with  temperature  except  for  B2O3,  the  dissocia- 
tion of  which  evidently  increases  very  rapidly  with 
temperature.  The  conductivity  of  KC1  or  NaCl  is 
very  nearly  proportional  to  the  absolute  temperature, 
that  of  KI  and  KBr  increases  a  little  more  rapidly, 
still  more  that  of  NaP03,  CaCl2  and  SrCl2,  that  of  Nal 


CONDUCTIVITY  OF  STRONG  ELECTROLYTES.        147 

and  the  silver  salts  more  slowly.  The  conductivity 
of  mixtures  of  equal  quantities  of  CaCl2  and  SrCk 
is  very  nearly  equal  to  the  mean  value  of  the  conduc- 
tivities of  the  two  components.  For  mixtures  of  KC1 
and  NaCl  the  conductivity  was  a  little  less  (1.5  to 
3  per  cent.)  than  calculated  according  to  the  said 
rule.  For  mixtures  of  NaP03  (x  per  cent.)  and  B203 
the  following  values  were  observed  at  900°  (d  is  density, 
c  concentration  in  gram  equivalents  per  liter,  A  equiva- 
lent conductivity,  t\  viscosity): 


X 

0 

0.5 

1 

5 

10 

25 

50 

100 

d 

1.520 

1.522 

1.552 

1.585 

1. 

655 

1.820 

2.115 

2.144 

c 



0.075 

0.15 

0.78 

1. 

62 

4.46 

10.35 

21.0 

A 



0.67 



1.55 



16.4 

49.5 

7;A 



74.3 



73.3 



73.8 

74.3 

The  product  TjA  is  very  nearly  constant.  From  this 
result  the  authors  conclude  that  probably  the  NaP03 
is  nearly  totally  dissociated  into  its  ions.  Goodwin  and 
Kalmus  also  found  TjA  for  fused  PbCl2,  PbBr2  and 
K2Cr2O7,  nearly  independent  of  temperature  and  thence 
concluded  that  fused  salts  are  subject  to  a  high  degree 
of  electrolytic  dissociation. 

The  concentration  and  equivalent  conductivity  at 
900°  of  some  salts  is  given  below: 

Salt  KC1  NaCl  CaCl,  SrCla  BaCla 

c  19.7  25.3  36.2  34.0  30.5 

A          123.5  144.5  64.1  58.2  56.1 

The  molecular  conductivity,  which  for  CaCl2,  SrCk 
and  BaCl2  is  2A,  is  of  the  same  order  of  magnitude  for 
the  five  fused  salts. 

A  great  number  of  investigators  have  found  that 
in  some  cases  solutions  behave  so  "abnormally"  that 
the  molecular  conductivity  instead  of  increasing  de- 


148  THEORIES  OF  SOLUTIONS. 

creases  with  dilution.  For  aqueous  solutions  this  ir- 
regularity has  been  observed  with  highly  diluted  solu- 
tions of  strong  acids  and  bases  and  is  explained  as  due 
to  the  presence  of  traces  of  impurities,  especially 
carbonic  acid,  hi  the  distilled  water,  used  for  the  dilu- 
tion. A  similar  explanation  seems  impossible  in  most 
of  the  other  cases  observed  with  solvents  other  than 
water  and  they  were  therefore  sometimes  considered 
as  a  proof  of  the  insufficiency  of  the  theory  of  electro- 
lytic dissociation.  A  clew  to  the  understanding  of 
these  "  abnormities "  was  found  by  Steele,  Mclntosh 
and  Archibald,  who  investigated  the  conductivities  of 
solutions  of  organic  substances  such  as  ethyl  ether  and 
acetone,  hi  HC1,  HBr  and  HI.  They  made  it  probable, 
that  some  molecules,  two  or  three,  of  the  dissolved 
substance  combine  with  one  molecule  of  the  solvent 
to  form  a  salt-like  conducting  compound.  According 
to  the  law  of  chemical  equilibria  the  number  of  con- 
ducting molecules  d  minishes  with  increasing  dilution. 
Hence  the  increased  dissociation  of  the  conducting 
molecules  with  increasing  dilution  may  be  more  than 
compensated  by  their  increasing  decomposition.  The 
said  authors  also  applied  this  idea  to  similar  cases 
observed  before  by  other  investigators. 

Similar  observations  were  made  by  I.  Wallace  Walker 
and  F.  Godschall  Johnson  on  solutions  of  KC1,  KI  and 
KCN  in  acetamide.  They  also  observed  the  migration 
of  the  ions  'n  these  cases  and  found  that  combinations 
of  the  salts  and  the  solvent  occurred. 

Some  very  instructive  similar  observations  have  been 
made  by  Foote  and  Martin.  They  found  the  following 
values  of  the  molecular  conductivity  /z  at  282°  C.  for 
solutions  of  1  gram-molecule  in  V  liters  of  HgCl2: 


CONDUCTIVITY  OF  STRONG  ELECTROLYTES.        149 

V=  2  5  15  20  30 

MforCsCl  70  51  48.5  44 

AiforKCl  81  62  45.7  43.4  38.5 

H  for  NHiCl  64.5  46.5  

MforNaCl  61.5  43.8  31.3  28.0  — 

/iforCuCl  70  42  26  24 

CuCl2  is  soluble  but  does  not  increase  the  conductivity 
of  the  solvent. 

Determinations  of  the  freezing  point  of  the  solutions 
indicated  that  the  depression  was  normal.  It  was 
therefore  necessary  to  suppose  that  molecules  of,  e.  g.t 
the  composition  HgCl2 .  NaaCk  were  formed  which  dis- 
sociate into  the  ions  Na  and  NaHgCL  The  presence 
of  similar  double  salts  and  complex  ions  in  solutions 
have  been  ascertained  in  many  different  ways,  as  for 
instance  the  solubility  of  HgCl2  or  HgI2  hi  solutions  of 
KC1  or  KI,  the  freezing  point  of  such  complex  solutions, 
the  diminution  of  the  catalytic  influence  of  KI  on  H2O2 
on  addition  of  HgI2,  the  distribution  of  HgI2  between 
a  solution  of  KI  in  water  and  benzene.  They  are  very 
well  known  in  crystalline  form.  This  is  a  good  example 
of  the  applicability  of  the  hypothesis  of  Steele,  Mcln- 
tosh  and  Archibald. 

Another  series  of  interesting  measurements  of  ab- 
normal dissociation  has  been  given  by  Walden  and 
Centnerszwer  for  solutions  of  potassium  iodide  in 
sulphur  diox  de.  They  found: 


y=  0.5 

1 

2 

4 

8 

16 

32 

M=38.2 

42.9 

44.9 

42.0 

35.6 

37.0 

41.3 

7  =  64 

128 

256 

512 

1,024 

2,048 

M=48.3 

57.5 

70.4 

86.7 

105.5 

126.0 

At  first  M  increases  in  the  normal  manner,  then  de- 
creases until  a  minimum  35.6  is  reached  at  V  =  8  and 
thereafter  increases  very  rapidly  again. 


150  THEORIES  OF  SOLUTIONS. 

This  field  was  in  a  high  degree  elucidated  by  Franklin 
and  his  pupils.  They  investigated  solutions  of  a  great 
number  of  salts  in  ammonia  and  organic  amines.  As 
an  example  I  give  the  figures  for  the  solution  in  NH3 
of  ammoniacal  zinc  nitrate  ZnN206  +  4NH3  at  —  33.5°. 

7=  0.999        1.539        1.961        2.520       3.051  3.891        7.717 

M=98.8  103.6  102.0          99.48  97.34  93.42  86.52 

7  =  15.25        30.10        59.46  117.6  182.2  358.0  707.2 

M =86.30        94.78  105.8  124.3  136.0  160.8  191.0 

Similar  cases,  with  first  a  maximum,  thereafter  a 
minimum  and  then  a  normal  increase  is  found  for 
solutions  of  copper  nitrate,  potassium  mercuricyanide 
and  potassium  amide  in  ammonia  and  silver  nitrate 
in  methylamine.  In  other  cases  (e.  g.,  AgN03,  LiN03, 
NH4N03  or  KI  in  NH3)  the  first  maximum  disappears 
and  is  replaced  by  an  inflexion  point  and  thereafter  an 
interval  of  nearly  constant  values  of  /*.  In  still  other 
cases,  e.  g.,  trimethylsulfonium  iodide,  metamethoxy- 
benzenesulfonamide,  orthonitrophenol,  trinitraniline, 
the  behavior  was  just  the  same  as  the  normal  one  in 
aqueous  solutions. 

The  first  increase  at  low  values  is  due  to  a  rapid 
increase  in  the  flu  dity  on  addition  of  ammonia,  the 
maximum  with  the  following  decrease  is  due  to  forma- 
tion of  molecular  complexes.  It  is  noteworthy  that 
this  maximum  is  most  obvious  just  for  solutions  of  salts 
of  heavy  metals,  which  as  early  as  1859  were  found  by 
Hittorf  to  contain  complex  ions,  especially  in  organic 
solvents  (ethyl  and  amyl  alcohol).  They  are  also 
known  to  give  complex  salts  with  ammonia.  After  the 
minimum,  the  quantity  of  ammonia  is  so  great  that  its 
concentration  may  be  regarded  as  nearly  constant; 


CONDUCTIVITY  OF  STRONG  ELECTROLYTES.        151 

then  the  concentration  of  the  conducting  compound  of 
ammonia  and  salt  is  nearly  proportional  to  the  quantity 
of  salt  and  the  conductivity  increases  in  a  regular 
manner.  Two  different  compounds  occur  in  these 
cases,  one  containing  a  less  percentage  of  ammonia 
and  a  better  conductor  (in  high  concentrations  of  the 
salt),  and  one  combined  with  a  greater  quantity  of 
NH3  and  a  poorer  conductor  (at  greater  dilutions). 
The  abnormality  with  the  minimum  may  then  simply 
be  due  to  the  greater  friction  of  the  more  voluminous 
4ons  rich  in  NH3  as  compared  with  that  of  the  ions  com- 
bined with  smaller  quantities  of  ammonia,  just  as  the 
friction  of  organic  ions  increases  with  their  complexity. 

A  Russian  chemist  A.  Ssacharow  investigated  solu- 
tions of  NH4I,  Lil,  AgN03  and  two  bromides  of  amides 
in  aniline,  mono-  and  dimethylaniline  and  observed 
some  cases  in  which  /*  decreased  with  increasing  dilu- 
tion. Evidently  these  solutions  are  very  nearly  related 
to  those  observed  by  Franklin. 

After  the  interesting  and  wide-reaching  investigations 
of  Franklin  similar  older  observations  of  Kahlenberg 
and  Ruhoff  regarding  the  abnormal  conductivity  of 
solutions  of  silver  nitrate  in  amylamine  are  easily 
understood.  The  assertion  made  by  these  authors, 
that  these  abnormal  conductivities  are  incompatible 
with  the  dissociation  theory,  is  therefore  eliminated. 

Even  in  fused  electrolytes  complex  salts  are  formed, 
which  must  be  taken  into  account  hi  calculations  re- 
garding their  conductivities.  Thus  R.  Lorenz  in  experi- 
ments regarding  the  migration  of  ions  found  that  in 
molten  mixtures  of  PbCl2  and  KC1  there  exist  com- 
pounds 2PbCl2 .  KC1,  PbCl2 .  2KC1  and  PbCl2 .  4KC1. 


152          THEORIES  OF  SOLUTIONS. 

One  of  the  most  experienced  investigators  regarding 
non-aqueous  solutions,  the  Italian  chemist  Carrara, 
comes  to  the  final  conclusion  that  the  same  laws  are 
valid  for  these  solutions  as  for  the  aqueous  ones  and 
that  the  conclusions  of  the  dissociation  theory  are 
applicable  and  can  explain  all  seeming  discrepancies 
hi  the  one  case  as  well  as  in  the  other.  Another  of 
the  most  experienced  men  hi  this  field,  Walden,  has 
expressed  the  same  opinion  in  nearly  identical  words. 


LECTURE  IX. 

EQUILIBRIA  IN  SOLUTIONS. 

THE  simplest  chemical  equilibrium  is  that  between  a 
gas  and  its  solution  hi  a  fluid,  which  is  expressed  by 
Henry's  law,  discovered  hi  1803.  This  law  states  that 
at  a  given  temperature  the  concentration  of  the  ab- 
sorbed gas  hi  the  fluid  phase  stands  in  a  constant 
proportion  to  that  of  the  gas  in  the  gaseous  phase. 
For  highly  soluble  gases  as  NH3  or  C02  the  law  is  not 
exact. 

A  similar  law  was  enunciated  by  M.  Berthelot  and 
Jungfleisch  for  the  partition  of  a  dissolved  substance 
between  two  liquid  phases  for  instance  iodine  between 
bisulphide  of  carbon  and  water  for  which  they  found 
(at  18°  C.) 

Gram  I  in  100  c.c.  water  per  cent.  0.041      0.032    0.016    0.010    0.009 
Gram  I  in  100  c.c.  CSa  per  cent.    17.4        12.9        6.6        4.1        0.76 
Ratio  1:424      1:403    1:412    1:410    1:400 

If  the  iodine  is  present  hi  so  great  quantity  that  it  is 
not  wholly  soluble  in  the  two  fluids,  concentrated  solu- 
tions are  formed  and  the  ratio  is  equal  to  the  quotient 
between  the  solubility  of  iodine  in  water  and  that  in 
bisulphide  of  carbon.  This  remark  was  made  by  Ber- 
thelot. 

Through  experiments  regarding  the  freezing  point  of 
solutions  it  has  been  proved  that  a  substance,  dissolved 
in  two  different  solvents,  generally  possesses  different 
molecular  weights  in  the  two  cases.  In  such  circum- 

153 


154          THEORIES  OF  SOLUTIONS. 

stances  the  simple  law  of  Berthelot  and  Jungfleisch  does 
not  hold.    Nernst  improved  it  by  attaching  the  con- 
dition that  the  law  is  true  for  only  the  same  kind  of 
molecules.    If  for  instance  benzoic  acid  in  water  con- 
sists (chiefly)  of  simple  molecules  C6H6COOH  and  in 
benzene  (chiefly)  of  double  molecules  (C6H5COOH)2, 
then  the  chemical  equilibrium  prevails: 
2C6H5COOH  (in  water)  ±;  (C6H5COOH)2  (in  benzene) 
and  the  law  of  Guldberg  and  Waage  demands: 
(concentration  in  water)2  =  constant  (concentration  in 

benzene). 

This  also  agrees  well  with  experience  as  indicated  by  the 
following  figures  (valid  at  20°). 

Cone,  in  water  d  0.097£    0.1500    0.1952    0.289  (g.  in  100  c.c.). 

Cone,  in  benzene  Cj  =     1.05        2.42        4.12        9.7 
Constant  =C2:cx»      =110         108         108         116 

For  more  dilute  solutions  the  number  of  electrolytically 
dissociated  molecules  in  the  aqueous  solution  and  of 
simple  molecules  in  the  benzene  solution  increases,  and 
the  equilibrium  cannot  be  calculated  in  the  simple 
manner  given  above,  but  a  closer  analysis  is  necessary. 
The  equilibrium  is  also  disturbed  by  the  circumstance 
that  a  small  quantity  of  water  is  soluble  in  the  benzene 
and  vice  versa,  and  this  quantity  depends  on  the  con- 
centration. 

The  said  law  has  been  of  great  use  in  determining 
the  partial  pressure  of  a  dissolved  substance  in  a 
solvent,  which  itself  possesses  a  perceptible  vapor 
pressure,  for  instance  of  water  in  ethyl  ether,  further 
for  determining  equilibria,  for  instance  between  NH3 
and  NH4OH  in  aqueous  solution.  If  namely  this  is 
shaken  with  chloroform,  the  NH3  molecules  are  divided 


EQUILIBRIA  IN  SOLUTIONS.  155 

between  the  water  and  the  chloroform,  but  the  NH4OH 
molecules  occur  only  in  the  aqueous  solution.  Moore 
used  some  figures  of  Dawson  and  MacCrae  in  which 
the  concentrations  were  the  following,  c  concentration 
of  ammonia  in  the  aqueous  phase,  Ci  concentration  in 
the  chloroform  phase,  x  concentration  of  NH3  in3he 
aqueous  phase,  y  concentration  of  NH4OH  in  the 
aqueous  phase,  the  concentration  of  the  ions  is  so  small 
that  it  might  be  omitted.  The  temperature  is  written 
under  t. 


t 
10° 

c 
0.3917 

0.01352 

x 
0.213 

15.8 

0.178 

0.836 

20° 

0.3917 

0.01588 

0.251 

15.5 

0.141 

0.560 

30° 

0.3917 

0.01846 

0.285 

15.4 

0.106 

0.372 

The  ratio  y  :  x  is  here  constant  at  a  given  temperature 
and  the  determination  of  x  is  therefore  not  possible 
simply  by  changing  c.  Therefore  experiments  at  dif- 
ferent temperatures  were  necessary.  According  to  the 
law  of  van't  Hoff  regarding  the  change  of  equilibrium 
with  temperature  it  is  possible  to  determine  the  change 
of  the  ratio  of  y/x  with  temperature,  if  we  know  the 
heat  evolved  on  the  addition  of  NH3  to  H20  so  that 
NH4OH  is  formed.  Moore  made  it  probable  that  x  :  d 
does  not  change  with  temperature  which  is  found  to 
be  true  in  this  and  similar  cases,  i.  e.,  that  no  perceptible 
heat  is  evolved,  when  in  the  experiment  NH3  passes 
from  an  aqueous  solution  to  a  chloroform  solution. 
This  gives  a  means  of  determining  the  ratio  y  :  x. 
(Moore  started  from  a  little  different  premises  and 
therefore  did  not  find  x  :  Ci  absolutely  constant.)  As  is 
seen  from  the  table  above  the  ratio  y  :  x  decreases 
rapidly  corresponding  to  a  heat  of  hydration  of  am- 
monia equal  to  7,190  calories.  The  dissociation  con- 


156  THEORIES  OF  SOLUTIONS. 

stant  was  found  to  be  about  k  =  5.10-5  at  20°  in  the 
equilibrium  equation  ky  =  22,  where  z  is  the  concentra- 
tion of  the  ions  NH4  and  OH.  This  constant  k  is 
evidently  (1  +  fe)  :  fcz  times  greater  than  that  found 
if  instead  of  the  concentration  y  of  NH4OH,  as  is  gener- 
ally done,  is  put  the  concentration  x  +  y  of  NH3  and 
NH4OH  together. 

The  law  of  partition  also  enables  us  to  determine  the 
molecular  weight  of  substances  hi  solid  solution.  For 
instance  thiophene  is  soluble  hi  solid  and  in  liquid 
benzene  and  the  partition  coefficient  is  independent  of 
the  concentration,  from  which  we  conclude  that  its 
molecular  weight  is  the  same  hi  both  cases.  Other 
experiments  have  been  carried  out  with  partition  of 
ethyl  ether  between  water  and  solid  naphthalene  and 
it  was  found  that  the  molecules  of  ether  in  naphthalene 
correspond  to  double  the  magnitude  of  that  given  by 
the  chemical  formula. 

Another  instance  of  the  use  of  the  partition  law  is 
found  in  studying  the  distribution  of  substances  be- 
tween cells,  e.  g.,  bacteria  or  blood-corpuscles  and  the 
surrounding  solutions.  In  this  manner  I  have  found 
that  ammonia  or  acetic  acid  or  saponine  possess  the 
same  molecular  weight  in  water  and  hi  red  blood- 
corpuscles.  We  can  not  decide  if  the  said  reagents  are 
united  with  some  substance  in  the  blood-corpuscles  but 
we  know  that  in  every  molecule  of  the  compound  just 
as  much  of  the  reagent  is  present  as  in  one  molecule 
of  it  in  the  surrounding  solution.  That  they  are  bound 
to  some  substance  in  the  blood  corpuscle  is  to  a  certain 
degree  probable  because  their  concentration  in  it  is 
between  a  hundred  and  a  thousand  times  greater  than  in 


EQUILIBRIA  IN  SOLUTIONS.  157 

the  liquid  in  which  it  is  suspended.  The  same  is  true  for 
the  absorption  of  so-called  agglutinins  in  just  those  bac- 
teria which  are  sensitive  to  them  and  of  so-called  im- 
mune-bodies in  red  blood-corpuscles.  In  these  two  cases 
a  high  degree  of  specificity  prevails  so  that  only  a  certain 
agglutinin  is  in  a  higher  degree  absorbed  by  a  given 
bacterium,  e.  g.,  coli-agglutinin  by  Bacterium  coli, 
cholera-agglutinin  by  cholera-vibrions  and  a  certain 
kind  of  red  blood-corpuscles  takes  up  a  given  immune- 
body,  namely  corpuscles  from  that  species  of  animals,  by 
the  injection  of  whose  corpuscles  in  the  veins  of  another 
animal  the  immune-body  in  question  has  been  produced. 
This  specificity  can  scarcely  be  understood  without 
supposing  a  chemical  reaction  of  the  cell-content  with 
the  reagent.  In  this  case  the  compounds  formed  con- 
tain only  two  thirds  as  much  of  the  reagent,  as  a  mole- 
cule of  it  in  the  surrounding  fluid.  It  was  urged  by 
the  school  of  colloid  chemists,  that  the  equation  of 
equilibrium  in  this  case: 

A  =  K  .  C0-67, 

where  A  is  the  concentration  of  the  absorbed  substance, 
C  its  concentration  in  the  surrounding  fluid,  indicates 
that  an  adsorption  phenomenon  prevails  here.  This 
might  be  true  for  a  small  variation  of  C,  but  in  the 
present  case  the  equation  holds  for  so  great  variations 
of  C  as  in  the  proportion  1  to  300  or  more  of  which 
there  is  no  example  in  the  adsorption  phenomena, 
except  perhaps  at  very  small  concentrations,  where 
proportionality  rules  between  A  and  C. 

The  most  important  of  all  equilibria  between  dis- 
solved substances  is  that  proved  for  weak  acids  by 


158  THEORIES  OF  SOLUTIONS. 

Ostwald.  The  law  of  mass  action  does  not  only  hold 
for  weak  monobasic  acids  as  acetic  acid,  but  as  well 
for  weak  di-  or  poly-basic  acids,  such  as  tartaric  acid 
or  citric  acid.  These  acids  are  so  weaK  that  only  one 
of  the  hydrogen  ions  is  dissociated  off  from  each 
molecule,  or  at  least  the  molecules  from  which  two 
hydrogen  ions  are  dissociated  away  are  so  small  in 
number  that  they  may  be  wholly  neglected. 

But  still  there  were  some  among  the  weak  acids,  such 
as  the  amidobenzoic  acids,  picolic  acid,  etc.,  for  which 
the  so-called  dissociation  constant  in  the  equation  of 
equilibrium  is  not  constant  but  changes  rather  rapidly 
with  dilution.  Ostwald  himself  supposed  that  perhaps 
the  explanation  ought  to  be  sought  for  in  the  circum- 
stance that  these  acids  may  also  act  as  weak  bases, 
so  that  a  salt-like  compound  might  be  formed  from  the 
two  molecules  of  the  acid. 

Such  substances  which  may  act  as  acids  towards 
bases  or  as  bases  towards  acids,  are  called  amphoteric 
electrolytes.  The  simplest  of  them  is  water,  which 
dissociates  into  the  hydrogen  ion  characteristic  for 
acids  and  the  hydroxyl  ion  characteristic  for  bases. 
Most  of  these  substances  are  amido  acids,  in  which  one 
hydrogen  atom  of  an  acid  is  replaced  by  the  group 
NH2  or  a  pyridine  residue  or  something  similar.  Also 
some  hydrates  of  metals  are  amphoteric,  e.  g.,  those  of 
lead,  aluminium,  zinc,  chromium,  arsenic,  beryllium,  tin, 
tellurium,  germanium.  These  last  substances  have  the 
formula  R  .  O  .  H,  which  gives  H-ions  as  well  as  OH- 
ions.  The  amino  acids  possess  the  formula  NH2RCOOH 
of  which  a  part  is  united  with  H20  to  OH .  NH3- 
RCOO .  H  just  as  a  part  of  NH3  is  bound  to  H20, 


EQUILIBRIA  IN  SOLUTIONS.  159 

thereby  giving  NH4OH.  The  molecule  OH .  NH3- 
R  .  COO  .  H  is  the  amphoteric  electrolyte;  it  may  dis- 
sociate off  hydroxyl-ions  from  its  NH3  side  and  H-ions 
from  its  COO-side.  It  may  even  give  off  both  and 
then  be  regarded  as  an  "inner  salt."  Bredig  was  the 
first  to  study  these  interesting  substances  and  he  in- 
duced his  pupil  Winkelblech  to  continue  this  investiga- 
tion. They  used  the  conductivity  and  the  hydrolysis 
of  the  salts  of  these  electrolytes  to  determine  the  dis- 
sociation constants  of  the  two  sides  of  these  molecules. 
These  researches  were  carried  much  further  by  James 
Walker,  who  gave  the  method  for  rationally  calculating 
the  degrees  of  dissociation  and  conductivities  of  these 
substances.  Finally  Lunde*n  has  performed  an  elab- 
orate experimental  work  and  written  a  monograph 
regarding  them.  As  an  instance  I  reproduce  the  fol- 
lowing table  regarding  meta-  and  ortho-aminobenzoic 
acid  (at  25°). 

META-AMIKORENZOIC  ACID. 

v.  a.106  d.105  fclQScalc.  *.10&ob§. 

64  11.8  159.0  1.12  1.12 

128  11.4  77.0  0.87  0.88 

256  10.7  36.2  0.81  0.84 

512  9.6  16.2  0.88  0.91 

1024  8.2  6.8  1.02  1.07 

OBTHOAMINOBENZOIC  ACID. 

v.                   0.106                 d.106             Jfc.lO»calc.  UO&obs. 

100      21.4      24.7      0.69  0.69 

200      17.6      10.1      0.80  0.81 

500      12.5       2.8      0.92  0.93 

1000      9.2       1.0      0.98  1.02 

In  these  tables  a  represents  the  concentration  of  the 
H-ions,  d  that  of  the  molecule  in  question  with  the  ion 
OH  thrown  off  (the  number  of  the  OH-ions  present  is 
determined  by  the  circumstance  that  the  product  of 


160  THEORIES  OF  SOLUTIONS. 

the  concentration  of  the  H-ions  with  that  of  the  OH- 
ions  is  constant  =  kw,  e.  g.,  0.31.10-14  at  10°,  10-14  at 
25°,  5.5. 10-14  at  50°),  v  is  the  volume  in  which  one  gram- 
molecule  is  diluted,  and  k  is  the  apparent  dissociation 
constant  calculated  from  the  conductivity  under  the 
supposition  that  the  two  acids  behave  as  other  acids. 
The  meta-acid  was  measured  by  Winkelblech  and  cal- 
culated by  Walker,  the  ortho-acid  was  measured  and 
calculated  by  Lunde"n. 

It  is  obvious  from  the  tables,  that  the  "dissociation 
constant"  k  is  not  constant,  but  also  that  this  agrees 
wholly  with  theory.  The  dissociation  constant  is  really 
double,  one  for  the  hydrogen-ions,  called  ka  (the  sub- 
stance regarded  as  an  acid)  and  one  for  the  OH-ions, 
called  kb  (the  substance  regarded  as  a  base).  These 
two  constants  were:  for  the  meta-acid  ka  =  1.63.10-5 
and  kb  1.23.10-11,  for  the  ortho-acid  ka  =  1.06.10-5, 
kb  =  1.37.10-12.  They  are  therefore  much  stronger  as 
acids  than  as  bases.  The  observed  k  is  rather  smaller 
than  the  real  ka',  the  amphoteric  character  lowers  the 
dissociation  of  H-ions  from  the  molecule.  The  meta- 
acid  is  stronger  than  the  ortho-acid  both  as  an  acid 
and  as  a  base.  Rather  remarkable  is  the  fact  that  the 
concentration  of  H-ions  for  the  meta-acid  is  nearly 
constant  between  v  =  64  and  v  =  256,  this  is  character- 
istic especially  when  kb  exceeds  very  much  the  value 
of  kw,  the  ion-product  of  water  at  the  same  temperature. 
For  a  value  ka  =  10-5  and  kb  =  1,000&W  Walker  has 
calculated  that  a  does  not  sink  more  than  from  9.99. 1CM 
to  9.44. 10-5  between  v  =  1  and  v  =  100,  whereas  d 
simultaneously  sinks  from  8,330.10-5  to  79.10-5.  If 
ka  =  kb  the  amphoteric  electrolyte  is  neutral,  i.  e., 


EQUILIBRIA  IN  SOLUTIONS.  161 

there  are  just  as  many  H-  as  OH-ions  in  the  solution. 
In  this  case  the  degree  of  dissociation  is  independent  of 
the  concentration  and  may  be  rather  high,  e.  g.y  for 
ka  =  10-7  the  degree  of  dissociation  is  0.667,  for  ka 
=  10-9  only  0.019  (no  such  substance  is  yet  known). 

Most  amphoteric  electrolytes  measured  are  stronger  as 
acids,  exceptions  are  :  acetoxim  ka  =  6.0. 10-13  and  kb  = 
6.5.10-13  at  25°,  ka  =  9.9.10-13  and  kb  =  19.0.10-13  at 
40°  and  histidin  ka  =  2.2.10-9  and  kb  =  5.7.10-9  at  25°. 
The  albuminous  substances,  such  as  albumine  from  eggs 
or  blood-serum,  globuline,  etc.,  seem  also  to  be  more 
acid  than  basic  substances,  they  give  salts  more  easily 
with  bases  than  with  acids.  The  same  is  the  case  with 
their  decomposition  products  leucin,  glycin,  and  alanin, 
for  which  ka  is  about  100  times  greater  than  kb)  and 
still  more  for  tyrosin,  leucylglycin,  alanylglycin  and 
glycylglycin,  which  are  about  1,000  times  stronger  as 
acids  than  as  bases.  The  peptones  and  still  more  casein 
are  very  decided  acids,  on  the  other  hand  the  prota- 
mins,  investigated  by  Kossel,  are  of  a  basic  nature. 

Robertson  has  made  some  interesting  applications  of 
the  theory  of  amphoteric  electrolytes  on  albuminous 
substances. 

The  chief  objection,  which  could  be  made  to  the  elec- 
trolytic dissociation  theory  at  first  glance, was  the  follow- 
ing. If  two  substances  are  mixed  with  each  other,  they 
may  generally  be  separated  from  each  other  by  means 
of  diffusion.  In  this  manner  it  was  for  instance  possible 
to  prove  experimentally  that  sal-ammonia,  NH4C1,  is  in 
the  gaseous  state  partially  decomposed  into  ammonia 
NHs  and  hydrochloric  acid,  HC1  (v.  Pebal).  But  it 
had  never  been  observed  that  the  ions,  into  which  a 
12 


162  THEORIES  OF  SOLUTIONS. 

salt  is  supposed  to  be  decomposed,  may  be  separated 
through  diffusion.  This  behavior  depends  on  the  cir- 
cumstance that  the  ions  of  a  salt,  e.  g.,  NaCl,  are  charged 
with  enormous  quantities  of  electricity  of  opposite  sign, 
Na  with  positive,  Cl  with  negative  electricity  to  the 
extent  of  96,550  coulombs  per  gram  equivalent.  If 
therefore  Na  and  Cl  separated  from  each  other,  power- 
ful electrical  attractions  between  the  Na  and  the  Cl 
atoms  would  carry  them  back  to  each  other,  as  I  re- 
marked in  my  inaugural  dissertation.  The  two  ions 
therefore  move  together  in  equivalent  quantities  through 
the  fluid,  as  if  no  dissociation  took  place. 

The  diffusion  of  salts  shows  a  certain  parallelism 
with  their  conductivity,  i.  e.,  with  the  mobility  of 
their  ions  as  has  been  especially  emphasized  by  Long 
and  Lenz.  This  question  could  not  be  cleared  up, 
before  it  was  regarded  from  the  point  of  view  of  the 
dissociation  theory,  which  was  done  by  Nernst  in  his 
well-known  investigation  on  the  mechanism  of  the 
diffusion  phenomenon.  There  he  proves  that  the 
rate  of  diffusion  is  equal  to  the  driving  osmotic  pressure 
divided  by  the  sum  of  the  frictions  of  the  ions  determined 
by  means  of  experiments  on  their  conductivities.  In 
this  manner  he  calculated  the  coefficients  of  dif- 
fusion and  found  them  in  very  good  agreement  with 
the  values  determined  experimentally.  Later  on  Oholm 
has  worked  out  this  chapter  with  the  best  of  success. 

It  may  be  remarked  here,  when  we  deal  with  the 
physical  applications  of  the  dissociation  theory,  that 
Nernst,  proceeding  further  along  the  same  lines  calcu- 
lated the  electromotive  forces,  which  arise  through 
the  unequal  diffusion  of  the  ions  in  so-called  concen- 


EQUILIBRIA  IN  SOLUTIONS.  163 

tration  cells,  which  had  been  before  treated  thermo- 
dynamically  by  Helmholtz.  In  this  case  the  powerful 
charges  of  electricity,  which  in  a  free  solution  hinder  the 
unequal  diffusion  of  the  two  ions,  are  carried  away 
by  means  of  unpolarizable  electrodes  dipping  into 
the  unequally  concentrated  parts  of  the  solution  and 
connected  metallically  with  each  other.  The  results 
found  by  Nernst  by  means  of  his  kinetic  views  agree 
wholly  with  those  arrived  at  by  Helmholtz.  Nernst's 
theory  has  been  unproved  by  the  work  of  Planck  and 
still  more  by  the  recent  work  of  Pleijel,  who  has 
solved  the  problem  in  its  entirety  and  removed  the 
mathematical  difficulties  which  hindered  its  complete 
solution  at  an  earlier  stage. 

The  theoretical  study  of  the  phenomenon  of  diffusion 
has  led  to  a  conclusion  which  seems  very  paradoxical. 
If  hydrochloric  acid  diffuses  in  water,  its  diffusion  con- 
stant is  found  to  be  2.09  at  12°  C.,  which  also  agrees  very 
well  with  the  theory  of  Nernst.  If  instead  of  using 
pure  water  for  the  diffusion,  I  take  a  solution  of  sodium 
chloride,  I  might  expect  that  the  molecules  HC1  moved, 
i.  e.j  diffused  more  slowly  in  that  medium  than  in  water 
because  of  the  increase  of  the  viscosity  on  addition  of  Na- 
Cl.  But  instead  of  that  an  increase  of  the  constant  of 
diffusion  is  observed.  For  instance  into  a  cylindrical 
vessel  was  poured  a  layer  of  1  cm.  height  of  1.04  n 
HC1  and  over  it  was  placed  pure  water  to  a  height  of 
3  cm.  The  diffusion  constant  was  found  to  be  2.09 
at  12°.  In  another  experiment  0.1  n  NaCl  was  used 
instead  of  water,  so  that  at  the  bottom  of  the  cylin- 
drical vessel  was  a  1  cm.  high  layer  1.04  n  in  regard 
to  HC1  and  0.1  n  in  regard  to  NaCl  and  over  it  were 
placed  3  cm.  of  0.1  n  NaCl. 


164  THEORIES  OF  SOLUTIONS. 

The  diffusionconstant  was  now  2.50.  According  to 
Nernst's  theory  I  calculated  2.43.  In  0.67  n  NaCl  the 
constant  was  still  higher  3.51,  calculated  3.47.  Many 
analogous  experiments  with  results  agreeing  with  the 
dissociation  theory  were  performed  with  nitric  and 
hydrochloric  acid,  caustic  potash  and  soda. 

The  explanation  is  that  when  the  H-ions  (i.  e.,  the 
acid)  diffuses  hi  pure  water  they  must  drag  the  (about 
5  times)  more  immobile  Cl-ions  with  them  in  equivalent 
number.  If  now  Na-ions  are  distributed  in  the  same  fluid, 
these  ions  are  carried  back  in  the  opposite  direction  of 
the  diffusing  H-ions  because  of  the  electric  forces  which 
hold  back  the  H-ions  and  pull  on  the  Cl-ions  in  the 
direction  of  diffusion  (upwards  hi  the  experiments). 
The  driving  back  of  the  Na-ions  partly  neutralizes 
these  electric  forces,  so  that  therefore  the  H-ions  are 
not  so  strongly  held  back  nor  the  Cl-ions  pushed  up  as 
in  pure  water.  Therefore  the  H-ions  diffuse  more 
rapidly  and  that  in  a  so  much  higher  degree  as  the 
Na-ions  are  more  numerous  relatively  to  the  H-ions. 
The  maximal  velocity  which  the  H-ions  may  reach  at 
12°  is  that  corresponding  to  no  hindrance  from  electrical 
forces  and  gives  a  diffusion  constant  6.17.  With  0.52  n 
HC1  and  3.43  n  NH4C1  I  reached  a  value  of  4.67  in- 
stead of  theoretically  calculated  5.72. — It  must  be  borne 
in  mind  that  at  these  high  concentrations  the  degree  of 
dissociation  of  the  HC1  is  diminished,  which  is  not 
taken  into  consideration,  and  therefore  the  observed 
dissociation  constant  is  smaller  than  the  calculated  one 
determined  with  the  supposition  that  the  electrolytic 
dissociation  is  complete. 

This  phenomenon  is  a  so-called  salt  action,  which  can 


EQUILIBRIA  IN  SOLUTIONS.  165 

not  be  explained,  if  we  suppose  the  molecules  of  the 
diffusing  acids  or  bases  and  the  added  salts  not  to  be 
dissociated  into  electrically  charged  ions.  It  is  a 
real  proof  of  the  electrolytic  dissociation  hypothesis. 

As  we  have  seen  above,  Guldberg  and  Waage,  hi 
their  theoretical  investigation  of  1867,  supposed  that 
foreign  subtances,  such  as  salts,  alcohol,  etc.,  exert  a 
certain  influence  on  reactions  without  actively  taking 
part  in  them,  and  they  introduced  into  their  formulae 
different  terms  to  account  for  this  action.  It  was 
especially  the  velocity  of  reaction  which  was  found  to 
depend  on  the  foreign  substances.  They  found  experi- 
mentally that  some  of  the  substances  accelerate  the 
reaction  (e.  g.,  NH4C1  the  solution  of  zinc  in  HC1); 
others  retard  it  (e.  #.,  ZnCl2  in  the  same  reaction). 
Van  Name  and  Edgar  found  that  KI  increases  the 
rate  of  solution  of  metals  by  means  of  iodine. 

Through  this  introduction  of  new  terms  the  equa- 
tions of  Guldberg  and  Waage  lost  their  simplicity  and 
the  many  empirical  constants  in  them  allowed  the  ar- 
rangement of  a  good  agreement  between  theory  and 
experience  but  thereby  the  correctness  of  the  theory 
was  not  subject  to  a  convincing  proof.  Therefore  at 
a  later  stage  they  threw  away  the  many  terms  and 
coefficients  having  reference  to  the  foreign  substances 
and  the  simple  law,  which  now  carries  their  name,  was 
the  excellent  result.  It  is,  of  course,  not  exact  for 
higher  concentrations  or  if  great  quantities  of  foreign 
substances  are  added. 

But  nevertheless  it  has  been  proved  that  the  salts 
exert  a  certain  influence  which  is  sometimes  very  great 
especially  on  the  velocity  of  reaction.  This  may  as 


166  THEORIES  OF  SOLUTIONS. 

we  now  know  be  of  rather  different  kinds  and  it  was 
therefore  quite  natural  that  Guldberg  and  Waage 
were  not  able  to  disentangle  this  complicated  riddle. 
The  simplest  case  is  the  action  of  a  sulphate  such  as 
potassium  sulphate  on  sulphuric  acid.  Then  a  part 
of  the  acid  is  bound  and  the  acid  sulphate  is  formed. 
Therefore  the  catalytic  action  of  the  sulphuric  acid 
is  diminished  by  the  addition  of  neutral  sulphates. 
Spohr  found  that  1  n  H^SO*  at  25°  has  a  reaction  con- 
stant equal  to  21.34  hi  inverting  cane  sugar.  On 
adding  0.5  n  K2S04  the  constant  decreased  to  16.07 
(i.  e.,  by  24.7  per  cent.),  on  adding  1  n  K2S04  the 
constant  was  only  11.56  (decrease  45.8  p.  c.). 

Quite  different  is  the  action  on  strong  monobasic 
acids.  The  velocity  of  inversion  by  means  of  0.25  n 
HBr  was  by  Spohr  found  equal  to  9.67;  an  addition  of 
0.5  n  KBr  or  1  n  KBr  increased  the  constant  to  12.18 
(26  p.  c.)  and  15.48  (60.1  p.  c.)  respectively.  This  pe- 
culiar action  will  be  treated  in  the  next  lecture  (p.  179). 

The  greatest  action  is  exerted  on  weak  acids  (e.  g., 
acetic  acid)  by  their  salts  (e.  g.,  sodium  acetate).  In 
this  case,  if  we  have  1  gram-molecule  of  acetic  acid  with 
the  degree  of  dissociation  a  and  n  gram-molecules  of 
NaCH3COO  with  the  degree  of  dissociation  0  in  V  liter 
solution,  the  following  equilibrium  holds: 

-  a)  V 


where  K  is  the  constant  of  dissociation  (1.8.10-5)  for 
acetic  acid  at  the  temperature  used  (25°).  a  is  very 
small  (less  than  1  p.  c.),  0  rather  near  unity.  1  —  a 
is  very  nearly  constant  (as  1).  The  greater  n  is,  the  less 
is  a  and  the  velocity  of  reaction,  which  is  nearly  pro- 


EQUILIBRIA  IN  SOLUTIONS  167 

portional  to  a.    I  found  the  following  values  of  the 
velocity  of  reaction,  p,  when  V  =  4: 

n=  0         0.05          0.1  0.2  0.5  1 

10V»  observed    =0.75        0.122       0.070       0.040       0.019    0.0105 
10»/>  calculated  =  0.74        0.129        0.070        0.038        0.017    0.0100 

This  peculiarity  can  scarcely  be  explained  without 
the  help  of  the  dissociation  theory,  which,  as  is  seen 
from  the  good  agreement  between  the  observed  and 
calculated  values,  agrees  very  well  with  experience. 

This  influence  of  foreign  ions  on  the  degree  of  dis- 
sociation also  plays  an  important  r61e  hi  chemical 
equilibria.  Such  a  one  is  the  equilibrium  which  takes 
place  on  mixing  equivalent  quantities  of  two  acids  and 
of  a  base.  The  stronger  acid  takes  the  greater  part 
of  the  base.  According  to  the  theory  of  Guldberg  and 
Waage  the  coefficient  of  partition,  the  so-called  avidity, 
ought  to  be  proportional  to  the  square  root  of  the 
relative  strengths  of  the  acids,  as  measured  by  means 
of  their  catalytic  action,  and  Ostwald  tried  to  verify 
this  theorem.  But  if  a  strong  acid  and  a  weak  one 
compete,  the  influence  of  the  ions  of  the  salts  and  of 
the  strong  acid  diminishes  the  degree  of  dissociation  of 
the  weak  acid  in  a  high  degree,  whereas  the  dissocia- 
tion of  the  strong  acid  is  nearly  undisturbed.  The 
consequence  is  that  the  weak  acid  appears  much  weaker 
than  according  to  Guldberg  and  Waage's  theory,  which 
did  not  consider  the  dissociation  of  electrolytes.  An 
exact  calculation  taught  me  that  the  avidity  of  an  acid 
is  not  proportional  to  the  square  root  of  its  catalytic 
action,  i.  e.,  its  degree  of  dissociation,  but  very  nearly  to 
this  action  itself,  and  this  theoretical  deduction  was  cor- 
roborated by  previous  experiments  by  Ostwald  as  the 


168          THEORIES  OF  SOLUTIONS. 

following  table  giving  the  fractions  of  the  bases  (NaOH, 
KOH  and  NH3)  taken  by  the  two  acids  indicates. 

Observed.  Calculated. 

Nitric:  dichloracetic 0.76  :  0.24  0.69  :  0.31 

Hydrochloric:  dichloracetic  .  .0.74  :  0.26  0.69  :  0.31 

Trichloracetic:  dichloracetic.  .0.71  :  0.29  0.69  :  0.31 

Dichloracetic:  lactic 0.91  :  0.09  0.95  :  0.05 

Trichloracetic:  monochlora- 

cetic 0.92  :  0.08  0.91  :  0.09 

Trichloracetic:  formic 0.97  :  0.03  0.92  :  0.08 

Formic:  lactic 0.54  :  0.46  0.56  :  0.44 

Formic:  acetic 0.76  :  0.24  0.75  :  0.25 

Formic:  butyric 0.80  :  0.20  0.79  :  0.21 

Formic:  isobutyric 0.79  :  0.21  0.79  :  0.21 

Formic:  propionic 0.81  :  0.19  0.80  :  0.20 

Formic:  glycolic 0.44  :  0.56 (?)  0.53  :  0.47 

Acetic:  butyric 0.53  :  0.47  0.54  :  0.46 

Acetic:  isobutyric 0.53  :  0.47  0.54  :  0.46 

This  is  one  of  the  best  proofs  of  the  usefulness  of 
the  dissociation  theory,  for  any  theory  which  does  not 
suppose  that  the  acid  molecules  are  dissociated,  gives 
calculated  figures,  which  are  nearly  proportional  to  the 
square  roots  of  those  given  above. 

Water  is  partly  electrolytically  dissociated.  There- 
fore it  reacts  with  salts,  dissolved  in  it,  and  hydrolyzes 
them  partially.  For  salts  of  a  strong  acid  or  base  with 
a  weak  base  or  acid  the  degree  of  hydrolysis  increases 
nearly  proportionally  to  the  square  root  of  the  dilution, 
as  was  also  shown  by  Shields  and  others.  For  salts  of 
weak  acids  with  weak  bases  the  peculiar  fact  is  deduced 
theoretically  that  if  the  dilution  is  not  extremely  great, 
the  degree  of  hydrolysis  remains  nearly  independent  of 
the  dilution.  This  was  also  found  by  Walker  for 
anilinacetate,  the  hydrolysis  of  which  did  not  increase 
more  than  from  54.6  per  cent,  to  56.9  per  cent.,  when 
the  volume,  in  which  one  gram-molecule  of  anilinacetate 
was  dissolved,  increased  from  12.5  to  800  liter. 


EQUILIBRIA  IN  SOLUTIONS.  169 

Now  Hantzsch  drew  the  conclusion  from  some  of  his 
experiments  that  salts  of  aliphatic  nitrocompounds  and 
of  isonitrosoketones  behave  abnormally  in  regard  to 
hydrolysis  and  supposed,  that  this  circumstance  was 
due  to  a  transformation  of  the  reacting  acids  or  bases 
into  then*  so-called  pseudo-forms.  This  assertion  does 
not  conform  to  the  theory  of  electrolytic  dissociation. 
A  little  later  also  Hantzsch  in  collaboration  with  Ley 
found  on  closer  examination  that  the  isonitrosoketones 
do  not  at  all  disagree  in  their  hydrolytic  properties 
with  the  dissociation  theory.  The  same  was  the  result 
of  an  investigation  by  Lunde*n  regarding  the  aliphatic 
nitro-compounds. 

A  certain  difficulty  for  the  dissociation  theory  seemed 
to  arise  from  an  investigation  of  Wakeman  regarding 
the  conductivity  of  weak  acids  hi  mixtures  of  alcohol 
(up  to  50  p.  c.)  and  water.  These  acids — acetic, 
cyanacetic,  glycolic,  monobromacetic  and  orthonitro- 
benzoic — obey,  in  aqueous  solution,  the  law  of  mass 
action.  Wakeman  found  that  the  dissociation  con- 
stant of  the  same  acids  in  mixtures  of  alcohol  and  water 
decreases  with  increasing  dilution,  which  would  then 
be  in  contradiction  to  the  dissociation  theory.  The 
same  was  also  found  for  cyanacetic  acid  in  a  mixture  of 
water  and  acetone. 

The  result  of  Wakeman  seemed  corroborated  by  an 
investigation  by  Lincoln  on  the  same  subject.  But 
nevertheless  their  observations  seem  to  have  suffered 
from  some  grave  systematic  experimental  error.  God- 
lewski  made  very  careful  measurements  on  just  the  same 
acids  as  Wakeman  and  found  that  these  weak  acids 
follow  the  demands  of  the  dissociation  theory  in  all 


170  THEORIES  OF  SOLUTIONS. 

mixtures  from  pure  alcohol  to  water.  He  found  the 
following  dissociation  constants  multiplied  by  105  for 
the  following  acids  (at  18°) : 

Alcohol,  percent....     0   10  20  30   4050    60    70    80    90    100 
Salicylic  acid  l&k...  100   95   83   57   3218    11      4.6   1.8  0.57   0.013 
Cyanacetic  acid  10*&  370  360  210 192 120  76.5  57.3  29.2 10.7  2.5     0.05 
Bromacetic  acid  10»A;  138 131   85   58   3520.510.2   5.7   1.7  0.43   0.015 

The  dissociation  constant  at  first  decreases  slowly, 
when  alcohol  is  added,  then  more  rapidly  and  when  the 
quantity  of  water  is  only  70  to  80  per  cent.,  the  dis- 
sociation constant  diminishes  quite  suddenly  on  further 
addition  of  alcohol.  The  order  of  the  acids  in  regard 
to  their  strength  is  not  the  same  in  alcoholic  as  in 
aqueous  solution.  The  dissociation  constants  in  alcohol 
are  about  10,000  times  smaller  than  in  water. 

The  most  violent  attack  on  the  modern  theories  or 
especially  on  that  of  van't  Hoff  is  found  in  a  memoir 
of  Kahlenberg.  He  determined  the  osmotic  pressure 
of  solutions  of  cane  sugar  in  pyridine,  separated  from 
pure  pyridine  by  a  membrane  of  caoutchouc,  which  is 
permeable  to  pyridine  but  not  to  cane  sugar.  He  found 
that  his  measurements  did  not  at  all  agree  with  the 
gas  laws  for  solutions.  These  measurements  were  re- 
peated by  Cohen  and  Commelin.  They  found  the 
experiments  connected  with  extremely  great  difficulties, 
which  had  caused  very  great  errors  in  Kahlenberg's 
measurements.  He  was  therefore  not  at  all  authorized 
to  draw  the  conclusions,  cited  above,  from  them. 

The  theories  of  the  analogy  between  the  gaseous  and 
the  diluted  state  of  matter  and  of  the  electrolytic  dis- 
sociation have  been  tried  with  perfect  success  in  so 
many  cases  and  found  to  be  of  such  great  use  as  well 


EQUILIBRIA  IN  SOLUTIONS.  171 

for  the  chemical  as  for  the  physical  and  even  the 
biological  sciences,  that  van't  HofFs  words  of  1890 
regarding  the  electrolytic  dissociation  theory  that  it  had 
become  nearly  a  fact  are  still  more  valid  now  than  20 
years  ago.  The  same  is  of  course  true  for  van't  HofPs 
theory  itself  which  is  indissolubly  connected  with  the 
dissociation  theory. 


LECTURE  X. 

THE  ABNORMALITY  OF  STRONG  ELECTROLYTES. 

THE  great  difficulty  in  the  application  of  Guldberg 
and  Waage's  law  to  the  equilibria  between  ions  and 
non-dissociated  salts  (acids  or  bases)  lies,  as  has  been 
said  above,  hi  the  great  deviation  of  the  strong  elec- 
trolytes, which  furthermore  are  of  the  greatest  impor- 
tance hi  nature  and  the  industries.  A  very  great  num- 
ber of  attempts  have  been  made  to  explain  this  devia- 
tion, but  none  of  them  has  to  this  day  been  crowned 
with  success,  and  I  therefore  give  only  a  short  review 
of  them.  They  may  be  grouped  chiefly  under  the  four 
following  headings: 

1.  Theories  introducing  a  correction  regarding  the 
change  of  the  ionic  friction  with  dilution. 

2.  Theories  introducing  a  correction  for  the  electric 
attraction  of  the  charges  of  the  ions. 

3.  Theories  regarding  the  influence  of  foreign  sub- 
stances on  the  osmotic  pressure  (the  so-called  salt- 
action). 

4.  Theories  regarding  the  binding  of  water  to  the 
ions. 

As  we  have  seen  above,  the  friction  of  the  ions  is,  if 
not  precisely  proportional  to,  yet  very  closely  related 
to  the  viscosity  of  the  surrounding  solution.  Now  for 
all  aqueous  solutions  of  salts,  except  those  of  NH4,  K, 
Rb  and  Cs — amongst  those  examined — the  viscosity 
increases  with  the  concentration.  If  we  corrected  the 

172 


ABNORMALITY  OF  STRONG  ELECTROLYTES.        173 

conductivity  for  the  viscosity,  we  would,  in  the  most 
cases,  obtain  a  by  far  higher  degree  of  dissociation  than 
that  calculated  in  the  usual  way  and  this  correction 
would  make  the  discrepancy  still  greater  than  before. 
The  deviation  takes  place  according  to  an  empirical 
law  found  by  van't  Hoff  (cf.  p.  133),  namely,  that  the 
dissociation  constant  in  the  equation  of  equilibrium 
increases  nearly  proportionally  to  the  square  root  of 
the  concentration  of  the  ions.  After  a  correction  the 
" constant"  would  increase  still  more  rapidly  with  con- 
centration— for  very  dilute  solutions,  below  0.1  normal, 
the  correction  would  be  of  very  small  importance.  Yet 
Jahn  advocated  a  theory  that  the  ionic  friction  increases 
very  markedly  with  dilution,  e.  g.,  by  about  13,  10  and 
8  per  cent,  for  K,  Na  and  H  ions,  when  they  are  diluted 
from  0.0334  normal  solution  to  infinite  dilution.  With- 
out further  explanation,  this  hypothesis  to  which  we 
come  back  a  little  later,  seems  inadmissible. 

The  ions  are  supposed  to  move  quite  freely  in  the 
solutions  and  therefore  to  exert  an  osmotic  pressure 
equal  to  that  of  an  equal  number  of  common  molecules, 
and  this  hypothesis  is  in  accord  with  the  observations 
regarding  freezing  and  boiling  points  of  solutions.  Now 
if  a  positive  ion  tried  to  fly  out  from  a  solution,  e.  g.,  into 
superposed  water  it  would  be  held  back  by  the  negative 
charge  of  the  rest  of  the  solution  and  hence  the  osmotic 
pressure  would  be  less  than  if  the  ions  were  wholly 
free.  This  diminution  of  the  osmotic  pressure  would 
for  each  ion  be  the  greater  the  less  the  distance  between 
the  ions,  i.  e.,  the  greater  the  concentration  was.  Now 
the  equation  of  equilibrium  indicates  (for  salts  of  two 
monovalent  ions,  such  as  KC1),  that 


174  THEORIES  OF  SOLUTIONS. 


where  the  osmotic  pressure  of  the  ions  is  indicated  by 
oiy  that  of  the  non-dissociated  salt  with  o.,  and  K  is  the 
constant  of  dissociation.  Now  oi  is  supposed  to  be 
proportional  to  the  concentration  ct  of  the  ions,  but 
according  to  the  electrostatic  attraction  theory  it  ought 
to  increase  more  slowly.  If  it  were  proportional  to 
c<0-75,  we  would  find  again  the  rule  found  by  van't  Hoff. 
In  reality  it  increases  according  to  another  law  and 
does  not  fit  very  well  with  the  experimental  determina- 
tions. The  greatest  objection  to  this  theory  is,  that 
it  would  demand  a  decidedly  smaller  lowering  of  the 
freezing  point,  especially  in  not  too  small  concen- 
trations, than  that  calculated  from  the  determinations 
of  the  conductivity.  The  deviation  from  the  theoretical 
law  is  in  the  opposite  direction  and  increases  with  con- 
centration. For  small  concentrations,  e.  g.,  up  to  0.2 
normal  for  KC1,  1  have  shown  that  theory  agrees  with 
experiment,  if  the  degree  of  dissociation  is  calculated  as 
proportional  to  the  molecular  conductivity. 

The  said  electrostatic  theory  has  been  developed  by 
v.  Steinwehr,  Liebenow,  Malmstrom  and  Kjellin. 

As  early  as  in  1788  Blagden  stated  in  an  excellent  in- 
vestigation that  the  freezing  points  of  aqueous  solutions 
in  general  are  proportional  to  the  concentration.  But 
in  some  cases,  e.  g.y  for  H2S04,  K2C03,  etc.,  he  observed 
that  the  lowering  of  the  freezing  increases  more  rapidly 
than  the  law  of  Blagden  indicates.  In  other  cases  the 
increase  was  less  than  according  to  the  law.  The  same 
was  found  by  Riidorff  in  1861,  and  stated  by  De 
Coppet  in  1871,  and  afterwards  by  many  others. 
Where  the  lowerings  were  less  at  high  concentrations 


ABNORMALITY  OF  STRONG  ELECTROLYTES.       175 

than  according  to  Blagden's  law,  this  could  easily  be 
explained  as  due  to  the  dissociation  which  diminishes 
with  increasing  concentration.  But  when  the  theory 
of  ionization  was  applied,  the  more  common  deviation 
in  opposite  direction  remained  unexplained. 

Rudorff  supposed  that  the  said  salts,  which  give  a 
too  great  lowering  of  the  freezing  point  hi  concentrated 
solutions,  bound  a  certain  part  of  the  water  as  water  of 
hydration,  e.  g.,  CaCl2  bound  6H20,  so  that  the  whole 
quantity  of  water  was  not  used  for  the  dilution.  This 
correction  helps  only  if  we  consider  the  concentration 
as  the  number  of  salt-molecules  in  100  g.  of  water  or 
in  100  molecules  of  water  and  of  salt,  and  not,  as  is 
common,  in  gram-molecules  per  liter.  The  idea  of 
Rudorff  was  carried  out  on  a  large  scale  by  H.  C.  Jones 
and  his  pupils,  with  due  regard  to  the  dissociation. 

From  these  determinations  it  was  calculated  that 
hydrates  were  formed  with  very  many  molecules  of 
water,  e.  g.,  the  chlorides  and  nitrates  of  bivalent  metals 
with  about  18,  the  corresponding  salts  of  trivalent 
metals  with  24,  glycerol  with  12,  cane  sugar  and 
fructose  with  6  molecules  of  water. 

Of  course  the  simplest  case  is  that  where  no  dissocia- 
tion takes  place,  i.  e.,  with  non-electrolytes.  These 
were  investigated  by  Abegg,  who  found  that  in  many 
cases  these  substances  give  an  increasing  molecular 
lowering  of  the  freezing  point  with  increasing  concentra- 
tion; in  other  cases  the  deviation  from  Blagden's  law 
was  in  the  opposite  direction. 

Some  very  accurate  experiments  regarding  the  os- 
motic pressure  of  solutions  of  cane  sugar  and  glucose 
were  performed  by  Morse  and  his  collaborators  and  by 


176  THEORIES  OF  SOLUTIONS. 

Berkeley  and  Hartley.  They  were  struck  by  the  nearly 
strict  proportionality  between  osmotic  pressure  and 
cpncentration  if  this  was  taken  according  to  Raoult's 
directions,  i.  e.,  in  gram-molecules  dissolved  in  100  g. 
of  water.  But  Sackur  showed  that  this  strict  propor- 
tionality occurred  only  at  about  20°  C.;  at  0°  C.  it  was 
necessary  to  suppose  a  binding  of  water  to  the  molecules 
of  sugar  (as  is  already  seen  from  Abegg's  work). 
Sackur  calculated  the  osmotic  pressure  p  from  the  data 
of  observations  with  the  help  of  a  modification: 

p(v  -  b)  =  RT 

of  van  der  Waals's  well-known  formula,  already  used  by 
Noyes.  v  is  the  volume  and  T  the  absolute  temperature 
of  the  solution  containing  1  gram-molecule,  R  is  the 
gas-constant  (1.985  cal.)  and  b  the  so-called  co volume. 
b  is  just  as  great  as  the  volume  of  the  dissolved  sugar 
at  23°  C.  (6  =  0.093  for  dextrose  and  0.20  for  cane 
sugar)  but  it  is  greater  at  0°  (0.16  and  0.31).  He 
found  the  following  values  of  1,000  6  at  0°. 


Methylalkohol 

Mol.     1,000  6. 
Weight 

..32        50 

Glycerol 

Mol. 
Weight. 

92 

1,000  &. 

106 

Ethylalkohol 

46        72 

Chloral 

1475 

125 

Acetone  

.  .58        55 

Dextrose.  .  .  . 

.180 

160 

Acetamide   . 

.  59        58 

Fructose 

180 

210 

Ethylformate  .  .  . 
Methylacetate  .  . 

..74      140 
..74        81 

Saccharose  .  . 

.342 

305 

In  general  6  increases  with  the  molecular  weight  and 
the  lowering  of  temperature.  Difficulties  arise  because 
sometimes  there  is  found  a  deviation  from  van't  Hoff  s 
law  even  in  very  dilute  solutions  (e.  g.f  hi  Abegg's 
figures),  and  Noyes  in  some  cases  found  negative  values 
of  6,  especially  in  non-aqueous  solutions. 


ABNORMALITY  OF  STRONG  ELECTROLYTES.        177 

The  question  of  the  formation  of  hydrates  in  solu- 
tions has  been  treated  in  a  masterly  manner  by  Wash- 
burn  in  a  monograph  to  which  I  refer  for  further  in- 
formation. 

A  very  interesting  phenomenon  has  been  discovered 
by  Svedberg.  He  investigated  the  validity  of  the  gas 
laws  for  suspensions  of  gold  or  mercury  (particles  of 
58.10-6  and  142.10-6  mm.  diameter  respectively)  and 
arrived  at  the  peculiar  result  that  these  suspensions  in 
extreme  dilutions  (3,700.106  and  1,500.106  particles, 
respectively,  per  cubic  centimeter)  obey  the  law  of 
Boyle,  but  that  in  10  and  15  times  respectively  greater 
concentrations  then*  osmotic  pressures  are  about  1.5 
and  2  times  respectively  greater  than  theory  demands. 
Here  there  is  no  question  of  the  impossibility  of  explain- 
ing these  deviations  by  supposing  the  formation  of 
hydrates,  the  quantity  of  water  bound  to  the  few  par- 
ticles of  metal  would  under  all  circumstances  be  abso- 
lutely insignificant. 

Tammann  measured  the  osmotic  pressure  of  cane 
sugar  solutions  to  which  he  had  added  0.91  mol. 
normal  solution  of  copper  sulphate.  This  solution  was 
on  the  outside  of  the  cell;  in  its  interior  was  a  solu- 
tion of  IQCeNeFe.  He  found  the  osmotic  pressure  of 
the  sugar  to  be  1.30  to  1.58  times  greater  than  the 
theoretical  value  (for  solutions  containing  0.04  to  0.06 
gram-molecule  per  liter).  Hence  the  osmotic  pressure 
of  the  cane  sugar  was  increased  by  an  average  of  40 
per  cent,  through  the  presence  of  the  copper  sulphate. 
Experiments  on  the  freezing  point  of  similar  solutions 
and  those  containing  no  copper  sulphate  gave  similar 
results.  The  same  was  the  case  with  solutions  of 
isobutyl  alcohol  in  the  presence  of 

13 


178  THEORIES  OF   SOLUTIONS. 

Other  experiments  were  performed  by  Abegg,  who 
measured  the  osmotic  pressure  by  the  aid  of  diffusion 
with  the  same  results  as  Tammann.  He  found  that  salts 
(NH4N03  and  NH4C1)  diffuse  from  an  aqueous  solution 
which  contains  a  little  quantity  of  alcohol  (2  normal) 
into  an  aqueous  solution  equally  concentrated  in  regard 
to  the  salts,  without  alcohol.  The  presence  of  the 
alcohol  was  therefore  found  to  increase  the  osmotic 
pressure  of  the  salt. — Evidently  this  is  the  same  phe- 
nomenon as  that  termed  salting  out  of  substances  from 
water. 

Quite  recently  Rivett  has  examined  this  peculiar- 
ity. He  investigated  solutions  containing  salts  and 
cane  sugar  and  found  that  if  the  described  increase  in 
the  lowering  of  the  freezing  point  is  attributed  to  the 
increase  of  the  osmotic  pressure  of  the  cane  sugar  this 
increase  is  proportional  to  the  product  of  the  quantity 
of  the  salt  and  that  of  sugar  present.  The  least 
influence  was  produced  by  barium  nitrate  which  hi  0.5 
equivalent  normal  solution  increased  the  osmotic  pres- 
sure of  the  sugar  by  only  4  per  cent.,  the  greatest  by 
lithium  chloride  which  in  0.5  equivalent  normal  solu- 
tion gave  an  increase  of  30.5  per  cent.  Similar  experi- 
ments were  made  with  ethyl  acetate  with  similar 
results  (changing  between  10  per  cent,  for  barium  ni- 
trate and  30  per  cent,  for  sodium  chloride  hi  0.5  equiva- 
lent normal  solution). 

Further  experiments  are  necessary  for  ascertaining 
if  an  increase  in  the  osmotic  pressure  of  the  salt  or  of 
the  cane  sugar,  respectively,  or  of  the  ethyl  acetate  or 
both  (which  is  probable)  has  taken  place. 

These  experiments  remind  very  much  of  the  influence 


ABNOKMALITY   OF  STRONG  ELECTROLYTES.         179 

of  salts  on  the  velocity  of  reaction  of  acids  acting  upon 
cane  sugar  or  ethyl  acetate.  This  velocity  is  increased 
to  a  high  degree,  about  30  per  cent,  on  adding  a  0.5 
equivalent  normal  chloride  or  nitrate  (for  inversion  of 
cane  sugar)  whereas  an  addition  of  methyl  or  ethyl 
alcohol  or  even  of  a  weakly  dissociated  electrolyte  such 
as  acetic  acid  or  chloride  of  mercury  has  no,  or  only  a 
very  small,  influence.  For  the  action  of  salt  on  the 
saponification  of  ethyl  acetate  by  means  of  acids  the 
effect  is  less,  about  12  per  cent,  for  0.5  n  chlorides  and 
only  4  per  cent,  for  0.5  n  nitrates.  In  saponification 
by  means  of  bases  the  action  is  very  small  and  different 
in  different  cases,  sometimes  negative.  The  action  is 
proportional  to  the  concentration  of  the  salt. 

Moreover,  the  dissociation  of  weak  acids  is  increased 
by  the  addition  of  neutral  salts,  which  indicates  an 
increase  in  the  osmotic  pressure  of  the  non-dissociated 
part  of  the  acid  by  the  presence  of  the  salt. 

The  solubility  of  different  substances  such  as  gases, 
e.  g.y  H2,  02,  CO,  N2,  NO,  or  organic  substances,  e.  g., 
ethyl  acetate  and  phenylthiocarbamide,  hi  water  is 
diminished  by  the  addition  of  salts  but  not  of  non- 
dissociated  substances,  which  may  be  explained  as  due 
to  an  increase  of  the  osmotic  pressure  of  those  sub- 
stances by  the  presence  of  these  salts.  Washburn  has 
given  a  review  of  this  action. 

All  these  phenomena  indicate  that  the  osmotic  pres- 
sure of  a  substance  is  in  a  high  degree  dependent  on  the 
presence  of  foreign  substances  especially  of  salts  in  the 
solvent  water.  Attempts  have  been  made  to  explain  this 
action  through  the  binding  of  water  to  the  salts,  but  the 
success  attained  has  been  very  moderate.  On  the  other 


180  THEORIES  OP  SOLUTIONS. 

hand  it  is  clear  that  if  the  ions  act  so  as  to  increase  the 
osmotic  pressure  of  non-dissociated  substances,  the 
dissociation  constant  of  salts  may  be  increased  by  the 
presence  of  its  own  ions,  i.  e.,  by  its  own  concentration, 
which  explanation  I  proposed  in  1899.  This  hypothesis 
has  been  taken  up  by  Partington.  He  concludes,  from 
the  great  ionizing  influence  of  free  ions  hi  gases,  that 
there  exists  a  similar  influence  of  free  ions  in  liquids  and 
shows  that  a  formula  deduced  from  the  ionization  of 
salts  from  this  idea  agrees  well  with  experience. 

Of  course  there  is  no  doubt  that  electrolytes  in  solu- 
tion bind  water.  Jones  showed  that  in  solutions  con- 
taining sulphuric  acid  and  water  dissolved  hi  acetic 
acid,  molecules  of  the  composition  H2S04  +  H20, 
H2S04  +  2H20  and  probably  H2S04  +  3H2O,  exist, 
which  are  yet  dissociated  hi  a  high  degree.  Heydweiller, 
who  investigated  the  specific  weight  of  different  solu- 
tions of  salts  hi  water,  expressed  his  results  by  the 
formula: 

A.  =  A.i  +  ».(!-  i), 

where  i  is  the  number  of  ions  (hi  gram  ions)  and  (1  —  i) 
is  the  number  of  undissociated  molecules  hi  one  gram- 
molecule.  A,  is  the  change  of  density  through  the 
addition  of  the  salt,  divided  by  its  concentration.  At 
is  evidently  a  constant  from  which  the  density  of  the 
ions  and  Bt  one  from  which  the  density  of  the  undis- 
sociated molecules  may  be  calculated.  This  latter 
density  was  found  sometimes  to  agree  with  that  of 
anhydrous  salts  not  only  for  salts  which  do  not 
crystallize  with  water,  e.  g.,  for  KN03,  KC103,  AgN03, 
but  also  for  salts  which  bind  water  strongly  such  as 


ABNORMALITY  OP  STRONG  ELECTROLYTES.        181 

LiCl,  CaI2,  etc.  In  other  cases  it  agreed  with  the  density 
of  known  hydrates  such  as  Na2S04  +  10H20,  NaBr  + 
2H20,  CaCl2  +  6H20,  MgCl2  +  6H20,  CuS04  +  5H20, 
BaCl2  +  2H20,  MgS04  +  7H20,  etc.  In  some  cases 
the  hydrates  indicated  in  this  manner  seem  to  contain 
more  water  than  the  solid  salt  hydrates  which  are  stable 
at  the  same  temperature,  but  generally  the  inverse  is 
true.  We  may  therefore  say  that  the  non-dissociated 
parts  of  dissolved  salts  are  hydrated  to  about  the  same 
degree  as  the  salt  in  the  solid  state  at  the  same  tempera- 
ture (under  normal  conditions). 

The  constant  A,  gives  the  density  of  the  ions.  Of 
course  there  are  always  two  ions  present,  one  positive 
and  one  negative,  and  A,  is  therefore  of  a  strictly 
additive  nature.  As  these  "density  modules"  of  the 
ions  are  of  a  high  practical  value  also,  I  reproduce  them 
here  (for  equivalent  weights) : 

Positive  ion:  H        NH|        Li        Na      K       Rb        Cs      Ag 

Density  module  -1.25-0.94-0.31+1.35   2.16     6.52     10.59   9.70 

Positive  ion:  ^Mg  KCa  HSr  ^Cu  HZn  ^Cd  KBa  ^Pb 
Density  module:  1.36  2.04  4.38  4.06  4.67  5.48  6.5310.37 

Negative  ion:  OH      CNS     C2H802  F         Cl        Br       I 

Density  module:      3.37     2.88    3.14  3.08     3.01     6.67     10.31 

Negative  ion:  N08      C108          I08     ^C03  HS04  ^CrO4 

Density  module:      4.56       5.78         16.04       4.92     5.51     6.53 

Aty  the  sum  of  the  two  modules  of  a  salt's  ions,  is 
always  greater  than  Bt,  the  corresponding  quantity  of 
the  undissociated  salt.  Therefore  we  conclude  that 
ionization  is  combined  with  a  contraction  of  volume. 
This  is  also  well  known  in  other  cases.  For  instance 
if  a  base  is  neutralized  with  an  acid,  both  in  highly 
diluted  solutions,  the  whole  action  consists,  as  has  been 
said  above,  in  a  combination  of  the  hydrogen  ions  of 


182          THEORIES  OF  SOLUTIONS. 

the  acid  with  the  hydroxyl  ions  of  the  base.  The 
accompanying  expansion  Av  is  dependent  on  tempera- 
ture t  in  a  rather  complicated  manner  as  is  indicated 
by  the  table 

t  0  10  20  30  100  110  120  130  140  °C. 
Ay  20.9  20.1  19.2  18.7  18.7  20.0  22.5  25.4  25.7  c.c. 

The  peculiar  behavior  that  a  minimum  occurs 
between  30°  and  100°  depends  upon  the  occurrence  at 
low  temperature  in  the  water  of  so-called  ice  mole- 
cules together  with  the  real  water-molecules.  The  ice- 
molecules  have  a  greater  volume  than  the  water  mole- 
cules, therefore  the  volume  of  neutralization  is  greater  at 
0°  than  at  30°.  Otherwise  the  neutralization  volume 
Av  would  without  a  doubt  increase  continually  with 
increasing  temperature.  These  figures  are  found  for 
the  neutralization  of  NaOH  with  HC1.  Ostwald 
investigated  the  neutralization  of  different  strong 
acids  with  KOH  and  NaOH  and  found  the  following 
neutralization  volumes: 

Acid  HN03    HC1    HBr    HL 

AyforKOE        20.0    19.5        19.6     19.8    average    19.7 

Ay  for  NaOH      19.8     19.2        19.3     19.5  "        19.5 

There  is  still  a  little  difference  between  the  figure  for 
KOH  and  NaOH.  If  it  is  real  or  depends  upon  experi- 
mental errors  is  difficult  to  decide. 

In  the  neutralization  of  weak  acids  Ostwald  found 
a  much  lower  Aw.  This  depends  upon  the  almost 
wholly  undissociated  state  of  these  acids.  The  expan- 
sion on  neutralization  is  here  equal  to  the  difference 
between  the  expansion  due  to  the  combination  of  the 
two  ions  OH  and  H  to  form  water  and  that,  which  oc- 
curs when  the  weak  acid  is  formed  from  its  ions. 


ABNORMALITY  OF  STRONG  ELECTROLYTES.        183 

Now  this  latter  may  be  determined  from  the  change 
of  the  electrolytic  dissociation  with  change  of  pressure. 
Fan jung  therefore  determined  the  conductivity  of 
weak  acids  under  high  pressures,  up  to  500  atm.,  and 
therefrom  calculated  the  volume  of  dissociation  of 
these  acids,  and  by  subtracting  that  from  the  neutrali- 
zation volume  of  strong  acids  with  KOH  or  NaOH  he 
calculated  the  neutralization  volume  of  the  weak  acids 
and  compared  his  results  with  those  found  directly  by 
Ostwald.  His  results  are  reproduced  below: 

SubiUnce.  Volume  of  Neutralization. 

Obs.  (Ostwald).       Calc.  (Fanjung). 

Formic  acid 7.7  c.c.  8.7 

Acetic  acid 10.5  10.6 

Propionic  acid 12.2  12.4 

Butyric  acid 13.1  13.4 

Isobutyric  acid 13.8  13.3 

Lactic  acid 11.8  12.1 

Succinic  acid 11.8  11.2 

Maleic  acid 11.4  10.3 

The  agreement  is  as  good  as  might  be  expected  con- 
sidering the  difficulty  of  the  experiments. 

Ostwald  also  determined  the  neutralization  volume 
of  ammonia  with  strong  acids  and  found  it  to  be 
26  c.c.  at  15°  C.  This  observation  indicates  that  in  the 
electrolytic  dissociation  of  ammonia  an  expansion  of 
6.4  c.c  occurs,  which  seems  at  first  not  to  be  in  accord 
with  the  general  fact  that  dissociation  is  followed  by 
contraction.  But  we  remember  that  at  15°  C.  am- 
monia consists  of  59.4  per  cent,  of  NH3  and  40.6  per  cent, 
of  NH4OH  (cf r.  page  155) .  The  dissociation  process  may 
here  be  regarded  as  consisting  of  two  combined  proc- 
esses, the  formation  of  NH4OH  from  the  59.4  per  cent. 
NH3  and  a  corresponding  quantity  of  water  and  then 


184  THEORIES  OP  SOLUTIONS. 

the  dissociation  of  NH4OH  into  NH4  and  OH.  This 
latter  process  may  be  accompanied  by  a  contraction  if 
the  first  process  causes  an  expansion  of  more  than  6.4  c.c. 

It  seems  peculiar  that  dissociation  is  accompanied 
by  contraction,  although  such  examples  are  known — 
the  simplest  is  perhaps  that  ice  has  a  greater  volume, 
but  probably  more  complex  molecules,  than  liquid 
water,  or  that  a  contraction  occurs  on  mixing  ethyl  al- 
cohol and  water.  Drude  and  Nernst  gave  the  follow- 
ing explanation.  The  free  energy  of  a  charged  par- 
ticle, such  as  an  ion,  is  the  less  the  greater  the  constant 
of  dielectricity  in  its  surroundings.  The  dielectric 
constant  of  water  is  very  high  and  increases  with  its 
compression.  Now  the  free  energy  tends  to  a  mini- 
mum, therefore  the  water  has  a  tendency  to  contract 
in  the  neighborhood  of  the  ions.  This  contraction 
is  sometimes  so  great  that  the  volume  of  the  solution 
is  less  than  that  of  the  water  contained  in  it.  Such 
a  contraction  on  ionization  has  also  been  observed  by 
Carrara  and  Levi  on  dissolving  electrolytes  in  methyl 
or  ethyl  alcohol  or  urethane,  and  by  Walden  on  dis- 
solving iodide  of  tetraethylammonium  in  different 
solvents.  In  this  latter  case  it  was  always  nearly 
the  same,  namely  13  c.c. 

Another  explanation  of  this  fact  has  been  given, 
namely  that  the  ions  may  bind  water  and  this  binding 
might  well  cause  a  strong  contraction.  This  idea  that 
the  ions  bind  water  might  be  elucidated  by  studying 
the  relative  conductivity  of  the  ions  and  especially 
if  the  ions  carry  water  with  them  in  electrolytic  experi- 
ments. Kohlrausch  had  through  the  close  coincidence 
of  the  temperature  variation  of  fluidity  and  electric 


ABNORMALITY  OF  STRONG  ELECTROLYTES.        185 

conductivity  of  salt  solutions  been  led  to  the  hypothesis 
that  the  ions  are  surrounded  by  an  "aqueous  atmos- 
phere." The  idea  was  developed  by  Bousfield  who 
applied  Stokes'  law  to  the  mobility  of  ions  in  their 
solutions.  The  friction  of  a  little  sphere  against  the 
surrounding  medium  is  proportional  to  the  viscosity 
of  that  medium  and  the  radius  of  the  moving  sphere. 
Now  the  atomic  volume  of  Li,  Na,  K,  Rb  and  Cs 
increases  from  the  first  to  the  last.  We  might  there- 
fore suppose  that  Li  should  move  more  easily  than  Na 
and  that  more  easily  than  K  in  a  very  dilute  solution, 
the  viscosity  of  which  may  be  considered  equal  to 
that  of  water.  In  reality  this  is  the  order  of  the  rate 
of  diffusion  of  these  metals  (9.5  for  Li,  7.3  for  Na,  4.9 
for  K,  4.7  for  Rb  and  4.6  for  Cs)  in  mercury,  but  the 
order  of  the  mobility  of  the  corresponding  ions  in 
aqueous  solutions  is  the  inverse,  which  peculiar  circum- 
stance has  ever  attracted  attention  as  being  difficult 
to  understand.  Bousfield  calculated  the  radii  of  dif- 
ferent ions,  which  according  to  Stokes'  law  ought  to 
be  characteristic  of  them  hi  order  that  they  should 
possess  the  conductivity  really  observed.  I  give  below 
a  reproduction  of  Bousfield's  table,  in  which  Ii8  is  the 
conductivity  of  the  ion  in  question  at  18°  C.  and  r  its 
radius  at  three  different  temperatures,  namely  —  2, 
+  18  and  +  38°  C.,  that  of  the  hydrogen  ion  at  18°  C. 
taken  as  unity,  a  is  the  temperature  coefficient  of  I  at 
18°.  For  a  comparison  I  have  introduced  into  the 
table  under  the  headings  lk  and  «t108  the  values  of  the 
conductibilities  of  the  ions  and  their  temperature  co- 
efficients multiplied  by  104  at  18°  according  to 
Kohlrausch  (Praktiscne  Physik.,  llth  ed.,  1910). 


186          THEORIES  OF  SOLUTIONS. 

Kohlrausch  has  given  some  other  figures  regarding 
these  magnitudes,  which  I  also  give  here  because  of 
their  great  usefulness.  They  are: 


Ion. 
Ik 

Cs            Tl            %Ca 
68          66          51 

H 

;cd      > 
16 

£Ra 

58 

Br           I 

67 

5CN 

56.6 

BrO8 
46 

at.104  

212        215        247 

2. 

15        5 

539        \ 

215        2 

21 

Ion. 

IO4             C1O4 

( 

:noa 

C«H5Oj 

I        /^OrO 

*4            / 

^C,04 

Ik          .       .  . 

48              64 

47 

31 

72 

63 

at.10*  

231 

r 

Ion. 

fo 

a.  10*. 

at  —  2. 

at  +  18. 

at  +  38. 

Ik'         ' 

ifc.10*. 

H  

318 

154 

0.801 

1.000 

1.196 

315 

154 

OH  

174 

179 

1.541 

1.828 

2.078 

174 

180 

NO3  

61.8 

203 

4.57 

5.145 

5.59 

61.7 

205 

I  

66.4 

206 

4.28 

4.79 

5.17 

66.5 

213 

CIO,  

57 

207 

4.99 

5.58 

6.01 

55 

215 

Cl 

65.4 

215 

4.41 

4.86 

5.16 

65.5 

216 

Rb  

67.9 

217 

4.29 

4.68 

4.96 

67.5 

214 

K      

74.6 

220 

4.53 

4.91 

5.17 

64.6 

217 

NH4  

63.7 

223 

4.64 

4.99 

5.23 

64 

222 

J^SO4.  .  .  . 

69 

226 

4.31 

4.61 

4.80 

68.4 

227 

Ag  

54.7 

231 

5.50 

5.81 

6.00 

54.3 

229 

}/£  Sr  

53 

231 

5.68 

6.00 

6.19 

51.7 

247 

F       ...    . 

45.5 

232 

6.63 

6.99 

7.20 

46.6 

238 

I03  

33.9 

233 

8.91 

9.38 

9.65 

33.9 

234 

CaHsOz 

34 

236 

8.95 

9.35 

9.58 

35 

238 

HBa 

57 

239 

5.38 

5.58 

5.68 

55.5 

239 

Yz  Cu 

49 

240 

6.27 

6.49 

6.60 

46 



Yz  Pb 

61.5 

244 

5.05 

5.17 

5.22 

61 

240 

Na  

43.5 

245 

7.15 

7.31 

7.37 

43.5 

244 

YL  Mg 

46.0 

255 

6.93 

6.91 

6.84 

45 

256 

i^Zn 

46 

256 

7.00 

6.91 

6.82 

46 

254 

Li.. 

.  33.4 

261 

9.68 

9.52 

9.33 

33.4 

265 

HCO3 70       269    4.72      4.54      4.39 

The  temperature  coefficient  of  the  fluidity  of  water 
at  18°  is  251. 10-4,  therefore  r  increases  with  temperature 
for  those  ions  which  have  a  smaller  a,  decreases  for 
ions  with  a>251.10-4.  The  table  is  therefore  arranged 
according  to  the  magnitude  of  a.  A  great  difficulty 
at  first  arises  in  supposing  that  the  radii  of  the  ions 


ABNORMALITY  OF  STRONG  ELECTROLYTES.        187 

increase  with  temperature  in  such  a  high  degree  as 
indicated  above  (the  cubic  temperature  coefficient  of 
expansion  of  fluids  seldom  reaches  0.001  and  the  linear 
coefficient  of  expansion  is  only  a  third  of  that  magni- 
tude) .  It  is  therefore,  according  to  Bousfield's  hypothe- 
sis, necessary  to  suppose  that  the  ions  bind  more  and 
more  water  the  higher  the  temperature  rises.  As  an 
example  we  cite  the  estimate  of  Bousfield  that  one 
molecule  of  NaOH  at  0°  attaches  19.9,  at  20°  22  and 
at  40°  25.7  molecules  of  H20.  This  conclusion  does 
not  at  all  agree  with  our  experience  regarding  the 
hydration  of  solid  salts,  which  always  decreases  with 
rising  temperature,*  nor  is  it  in  accordance  with  the 
electrostriction  theory  for  the  dielectric  constant  of 
water  decreases  rapidly  with  increasing  temperature. 
The  Li-ion  with  its  aqueous  envelope  ought  to  be  eight 
times  as  great  as  that  of  the  Rb-ion  or  the  Cs-ion 
(/is  =  68) ;  it  ought  then  to  bind  a  very  great  number  of 
water  molecules.  The  K-ion,  which  seldom  enters  into 
solid  salts  with  crystal  water,  ought  to  bind  a  rather 
great  number  of  water  molecules  in  order  that  the  com- 
plex should  get  a  greater  radius  than  the  Rb-  or  Cs-ion. 
(The  atomic  volume  of  these  metals  hi  the  solid  state 
is  for  Li  13.1,  for  Na  23.7,  for  K  45.5,  for  Rb  56,  and 
for  Cs  71  cubic  centimeters.)  In  the  same  manner 
the  F-ion  has  a  greater  volume  than  the  Cl-ion  and  this 
exceeds  the  I-ion.  Otherwise  the  ions  possess  in  general 
the  less  mobility  the  more  composite  they  are,  as 
Ostwald  at  first  showed  for  ions  of  organic  acids,  and 
Bredig  for  the  corresponding  ions  of  bases. 

*  An  exception  from  this  law  has  been  related  by  Koppel  for  sulphate 
of  cerium  (Zeitschrift  fur  anorganische  Chemie,  41,  377  (1904)).  It 
is  well  worth  a  reinvestigation. 


188  THEORIES  OF  SOLUTIONS. 

The  work  of  Bousfield  leaves  us  in  ignorance  of  the 
precise  quantity  of  water  which  is  attached  to  each 
ion,  it  only  indicates  that  it  ought  to  be  very  great. 
This  want  has  been  removed  by  the  more  recent  work 
of  Buchboeck,  Washburn  and  Riesenf eld  and  Reinhold. 

It  is  possible  to  decide  if  water  is  dragged  with  the 
ions  if  they  wander  in  a  non-aqueous  medium  which  is 
diluted  by  addition  of  water.  The  main  parts  of  the 
liquid  are  not  altered  but  in  the  neighborhood  of  the 
electrodes  the  transported  water  is  deposited  and  may 
be  determined  according  to  the  method  of  Hittorf. 
Nernst,  Garrard  and  Oppermann  were  the  first  to  use 
this  method.  They  dissolved  boric  acid  in  the  solutions 
to  be  examined,  and  determined  if  the  concentration 
of  the  boric  acid  changed  during  the  passage  of  the 
current.  The  analytical  method  used  was  not  exact 
enough  to  allow  evident  conclusions.  The  same  was 
the  case  with  some  later  investigators  in  this  field  until 
Buchboeck  took  up  the  problem.  He  used  mannite 
and  resorcine  as  indicators.  He  electrolyzed  hydro- 
chloric acid,  which  after  the  experiment  was  removed 
from  a  sample  of  a  given  volume  by  means  of  silver 
carbonate  and  consequent  treatment  with  sulphureted 
hydrogen  to  remove  traces  of  silver,  after  which  the 
mannite  or  resorcine  present  was  determined  by  evapo- 
rating and  weighing.  Washburn  used  arsenious  acid, 
raffinose  or  saccharose  as  indicators  and  determined 
the  concentration  of  these  latter  simply  by  measuring 
the  rotatory  power  of  the  solution  before  and  after 
the  electrolysis. 

Of  course  it  is  necessary  to  know  that  the  indicator 
is  not  carried  forward  by  the  current  in  the  same 


ABNORMALITY  OF  STRONG  ELECTROLYTES.        189 

manner  as  colloids.  Indeed  there  are  some  experi- 
ments by  Coehn  which  seem  to  indicate  such  a  trans- 
port of  cane  sugar  and  probably  raffinose  behaves  hi 
the  same  manner.  In  all  cases  Washburn  stated  that 
with  his  experimental  arrangements  no  such  effect 
could  be  observed.  The  indicators  should  also  not 
unite  with  the  dissolved  salts  and  enter  into  complex 
ions,  nor  enter  into  reaction  with  substances  deposited 
at  the  electrodes  through  the  electrolysis.  For  this 
latter  purpose  unpolarizable  electrodes  of  silver  with 
a  coating  of  silver  chloride  were  used  and  the  elec- 
trolytes were  chlorides  (of  H,  Li,  Na  and  K).  The 
concentration  of  the  indicator  always  increased  in  the 
neighborhood  of  the  anode,  whereby  a  transport  of 
water  in  the  direction  of  the  current  is  indicated. 

The  effect  is  a  differential  one.  If  the  two  ions 
migrate  with  the  same  velocity  and  carry  each  the 
same  number  of  water  molecules,  then  the  concentra- 
tion of  the  water  will  not  change.  Therefore  we  must 
make  a  hypothesis  regarding  the  number  of  water 
molecules  transported  by  the  one  ion  in  order  to  deter- 
mine the  number  of  water  molecules  transported.  If 
it  is  supposed  that  the  chlorine-ion  does  not  carry  any 
water,  Washburn's  figures  give  the  following  values  for 
the  positive  ions: 

H  +  0.28  H20,  K  +  1.3  H20,  Na  +  2.0  H20,  Li  +  4.7 

H20. 

If  we  suppose  that  Cl  carries  one  molecule  of  water, 
we  must,  as  is  easily  seen,  add  to  the  0.28  molecule  of 
water  combined  with  the  H-ion,  as  calculated  above, 
a  quantity  inversely  proportional  to  the  relative  veloc- 


190  THEORIES  OF  SOLUTIONS. 

ity,  i.  e.,  in  this  case  65.5  :  315  =  0.2  (cfr.  p.  134, 
Washburn  gives  the  ratio  0.185).  The  corresponding 
figures  for  K,  Na  and  Li  are  according  to  Washburn 
1.02,  1.61  and  2.29.  Thus  for  instance  if  we  suppose 
that  the  chlorine-ion  carries  six  molecules  of  water, 
then  the  Li-ion  carries  4.7  +  6.2.29  =  18.5. 

It  is  clear  that  this  transportation  of  water  has  in- 
fluenced the  concentration  of  the  solutions  in  which 
Hittorf  and  his  successors  determined  the  migration  of 
ions.  At  extreme  dilution  this  difficulty  disappears, 
for  then  the  change  of  the  relative  concentration  of  ^'the 
water  through  its  transportation  becomes  inappreciable. 
Now  there  has  been  worked  out  by  Denison  and 
Steele  a  new  method  for  directly  measuring  the  velocity 
with  which  the  ions  proceed  by  means  of  optical  re- 
actions which  they  cause.  These  investigators,  for 
instance,  passed  a  current  through  three  solutions  of 
LiCl,  KC1  and  KCH3C02,  so  that  the  slower  ion  Li  or 
C2H302  followed  the  more  rapidly  moving  ion  K  or 
Cl  respectively  in  the  direction  of  then*  movement. 
Then  no  mixing  of  the  solutions  occurred  and  their 
boundary  surfaces  remained  sharp  and  could  be  deter- 
mined by  a  telescope  through  the  change  of  the  refrac- 
tive indices  in  them.  These  boundary  surfaces  move 
with  the  same  velocity  as  the  ions  K  and  Cl  in  the 
middle  portion  of  the  conducting  solution.  This 
method  is  independent  of  the  concomitant  transporta- 
tion of  water. 

From  his  own  experiments  Washburn  determined  the 
ratio  of  migration  of  the  positive  ion  according  to  the 
chemical  method  used  by  Hittorf,  then  corrected  it 
with  regard  to  the  transportation  of  the  water  and 


ABNOBMALITY  OF  STRONG  ELECTROLYTES.        191 

compared  it  with  the  results  of  Denison  and  Steele. 
He  found  for  1.25  normal  solutions  of  KC1  and  NaCl 
at  25°  the  following  values: 

Hittorf  a  Method.    Corrected.         Denison-Steele's 

Method. 

KC1 0.482  0.495  0.492 

NaCl 0.366  0.383  0.386 

The  figures  of  Denison  and  Steele  are  properly  valid 
for  1  n  solutions  at  18°,  but  the  difference  between 
these  solutions  and  1.25  n  at  25°  is  in  this  regard  in- 
significant. 

This  confirmation  of  the  correctness  of  Washburn's 
views  and  determinations  seems  very  valuable,  other- 
wise one  would  not  have  been  quite  certain  that  a 
part  of  the  sugar  or  raffinose  or  arsenious  acid  had  not 
wandered  also,  as  negative  ion-compounds  of  alkaline 
salts  with  sugar  are  well  known,  and  may,  to  a  small 
extent,  exist  in  aqueous  solution. 

Even  Washburn  could  not  with  the  means  at  his 
disposal  decide  how  great  a  quantity  of  water  is  at- 
tached to  the  ions,  but  only  that  Li  carries  more  water 
than  Na,  Na  than  K  and  K  than  H,  and  that  there  is 
certainly  a  transportation  of  water  with  the  ions.  The 
order  of  the  ions  Li,  Na  and  K  is  the  same  as  that  of 
their  solid  salts  hi  regard  to  their  capacity  for  binding 
water. 

A  new  step  was  taken  by  Riesenfeld  and  Reinhold. 
They  combined  the  methods  of  Washburn  and  Bous- 
field.  If  in  a  salt  ak  composed  of  the  anion  a  and 
the  cation  k,  these  two  ions  contribute  to  the  conduc- 
tivity with  the  fractions  wa  and  (1  —  w?a)  and  if  the 
anion  carries  A  molecules  and  the  cation  K  molecules  of 
water,  then  the  number  x  of  water  molecules  transported 


192 


THEORIES  OF  SOLUTIONS. 


to  the  anode,  accessible  to  analysis  after  the  passage  of 
96,550  coulombs  is  as  is  easily  seen: 

waA  -  (1  —  wa)  K  =  x. 

From  the  change  of  the  migration  rate  na)  as  deter- 
mined by  Hittorf,  with  concentration  it  is  possible  to 
determine  x,  as  Washburn  pointed  out,  for 

na  =  wa  +  x/a, 
if  1  equivalent  of  salt  is  dissolved  in  a  molecules  of 


0.5Z 


o.so 


0.40 


0.75 


O.Z       0.4       0.6        0.8        10 


10 


ABNORMALITY  OF  STRONG  ELECTROLYTES.        193 

water.  In  the  accompanying  diagrams  the  variation 
of  na  with  concentration  (c  =  55.5/a  for  dilute  solu- 
tions) is  represented. 

Further,  Biesenfeld  and  Reinhold  supposed  that  the 
number  of  water  molecules  combined  with  an  ion  is 
so  great  —  as  we  have  seen  BousfiehTs  figures  indicate 
that  this  number  is  generally  very  high  —  that  the 
volume  of  the  ion  with  accompanying  water  is  propor- 
tional to  this  number.  In  this  case  the  velocities  of 
the  ions  are  inversely  proportional  to  the  radii  of  these 
volumes,  i.  e.,  to  the  cube  root  of  the  accompanying 
number  of  water  molecules  A  and  K.  Hence  as  x  is 
known  we  have  two  equations  for  determining  A  and 
K,  and  we  may  calculate  both  of  them.  Riesenfeld 
and  Reinhold  now  calculated  the  number  of  water- 
molecules  attached  to  the  8  ions  entering  into  the 
electrolytes  HC1,  KN03,  AgN03,  CdS04  and  CuS04, 
for  which  x  is  relatively  well  determined.  From  these 
figures  they  calculated  seven  values  for  the  number  of 
H20  molecules  bound  to  the  ion  Cl  by  comparing  its 
conductivity  with  those  of  the  seven  other  ions.  They 
found  values  varying  between  16  and  24  with  an  average 
value  of  21.  With  the  aid  of  this  value  and  the  known 
conductivities  of  the  ions  they  found  the  following 
numbers  of  water  molecules  accompanying  each  ion: 


Ion:  .......................  H  K     Ag    ^Cd  HCu     Na    Li 

Number  of  H2O-molecules:  ....0.2  22     37       55         56        71     158 

Ion:  .......................  OH  y2SO<   Br     I  Cl    NO3   C1O3 

Number  of  H20-molecules:  ....  11  18      20     20  21      25      35 

It  is  of  course  impossible  to  suppose  that  a  lithium-ion 
is  chemically  bound  to  158  molecules  of  water.  It  is 
perhaps  bound  to  one,  two  or  three  molecules  of  water 

14 


194  THEORIES  OF  SOLUTIONS. 

as  the  solid  salts  LiCl  +  H20,  LiBr  -f  2H20  and 
Lil  +  3H20,  or  if  we  reserve  one  H20  for  the  anion, 
the  Li-ion  may  be  bound  to  about  2H20.  It  is  proba- 
ble that  hi  the  solution  there  occur  Li-ions  bound  to  1 
to  3  molecules  of  water.  The  motion  of  a  complex 
molecule  H20  —  Li  —  H20  may  be  estimated  to  cause 
about  double  the  effort  of  dragging  Li  alone.  There- 
fore the  mobility  of  Li  is  only  about  one  half  of  that 
of  Cs,  which  moves  the  most  rapidly  of  all  monovalent 
ions.  In  this  case  we  except  the  ions  H  and  OH  of  the 
water  HOH  itself  on  grounds  cited  above  (cf.  p.  134). 
The  friction  of  the  Na-ion  1/43.5  =  0.023  lies  about 
midway  between  that  of  Li  (1/33.4  =  0.03)  and  that  of 
Cs  (1/68  =  0.0147).  Hence  we  conclude  that  the  Na- 
ions  are  on  an  average  bound  to  about  one  molecule  of 
water.  The  other  monovalent  ions  are  bound  to  greater 
or  less  quantities  of  water,  which  as  averages  generally 
are  fractions  lying  between  zero  and  about  two.  With 
rising  temperature  the  number  of  water  molecules  bound 
to  the  ions  dissociate  off;  they  then  approach  the  limit 
value,  which  is  characteristic  for  ions  without  "ionic 
water."  Therefore  the  molecular  conductivity  of  dif- 
ferent monovalent  ions  converge  towards  a  common 
value  with  rising  temperature.  The  bivalent  ions  ought 
to  converge  to  double  this  value,  as  Noyes  has  also 
stated  for  S04. 

Now  Washburn  has  found  that  Li  drags  with  it  about 
5  molecules  of  water  which  at  first  seems  to  conflict 
with  the  assertion  that  on  an  average  Li  has  only  two 
molecules  of  "ionic  water."  But  as  is  well  known  from 
the  doctrine  of  the  fluidity  a  small  particle  moving  in 
water  carries  with  itself  a  rather  thick  "water  envelope." 


ABNORMALITY  OF  STRONG  ELECTROLYTES.        195 

The  molecules  of  water,  with  which  the  moving  par- 
ticle collides,  also  get  a  pull  in  the  direction  of  the  moving 
particle  and  are  carried  with  it.  Evidently  the  number 
of  water  molecules  dragged  in  this  manner  increases 
with  the  complexity  of  the  ion  and  therefore  also  with 
the  number  of  ionic  water  molecules. 

That  only  a  very  small  number  of  water  molecules 
is  bound  to  the  ions  is  evident  from  then*  very  marked 
individuality  in  moving  through  the  water,  especially 
if  we  consider  the  influence  of  the  temperature  on 
the  mobility.  The  number  of  water  molecules  dragged 
with  the  ions  may  of  course  be  considerably  greater. 

An  inspection  of  the  values  given  by  Bredig  regarding 
conductivities  of  organic  ions  consisting  of  a  great 
number  of  atoms,  shows  that  their  conductivities  are 
roughly  inversely  proportional  to  the  third  root  of  the 
number  of  atoms  contained  in  the  molecule.  This 
behavior  corresponds  to  the  law  of  Stokes. 

The  hydration  of  a  dissolved  substance  increases 
with  dilution.  Therefore  we  should  also  suppose  that 
the  average  number  of  ionic  water  molecules  increases 
with  dilution.  The  conductivity  of  the  ions  decreases 
very  rapidly  with  the  increasing  number  of  ionic  water 
molecules.  Therefore  the  degree  of  dissociation  calcu- 
lated from  the  conductivity  does  not  change  so  rapidly 
with  dilution  as  we  might  expect  if  we  did  not  consider 
the  diminished  mobility  at  high  dilutions.  The  idea  of 
Jahn  (cfr.  p.  173)  may  therefore  be  considered  right,  if  it 
is  combined  with  the  idea  of  hydration  which  is  undoubt- 
edly right.  I  regard  this  change  of  mobility  and  the 
salt  effect  as  the  chief  factors  which  disturb  the  validity 
of  Guldberg  and  Waage's  law  hi  its  application  to 
strong  electrolytes. 


LECTURE  XI. 

THE  DOCTRINE  OF  ENERGY  IN  REGARD  TO  SOLUTIONS. 

THE  free  energy  of  a  dissolved  substance  is  according 
to  van't  HofTs  law  just  as  great  as  the  free  energy  of 
the  same  quantity  of  matter  in  gaseous  form  per  gram- 
molecule,  i.  e., 

A  =  RTlo&p-RTlogepa  (1) 

where  R  is  the  gas  constant  1.985  cal.,  T  the  absolute 
temperature  and  p  the  osmotic  pressure.  This  formula 
indicates  the  work  done  in  compressing  one  gram-mole- 
cule of  a  gas  from  the  pressure  pa  to  the  pressure  p.  If 
pa  is  put  equal  to  1  then  log,  pa  =  0  and 

A=RTlo&p  (la) 

According  to  the  definition  of  free  energy,  A  is  therefore 
in  this  case  the  free  energy  of  the  said  mass  of  gas,  if 
the  free  energy  of  the  same  mass  of  gas  at  normal  pres- 
sure, e.  g.,  one  millhn.  mercury  is  taken  as  zero,  from 
which  the  free  energy  is  counted. 

If  we  have  to  calculate  the  change  of  free  energy  on 
evaporating  a  liquid,  we  consider  that  the  work  done 
in  lifting  a  piston  of  cross-section  s  cm.  square,  loaded 
with  p  kilograms  per  cm.  square,  i.  e.y  with  a  total  load 
of  ps  kilograms,  through  a  height  h  is 

psh  —  pv 
where  v  is  the  volume  passed  through  by  the  piston. 

196 


THE   DOCTRINE   OF   ENERGY.  197 

If  we  allow  the  vapor  to  lift  the  said  piston,  the  volume 
v  is  filled  with  saturated  vapor.  If  th  e  evaporated  quan- 
tity is  one  gram-molecule,  the  work  done  is: 

pv  =  RT. 

By  this  quantity  the  free  energy  of  the  said  unit  quan- 
tity of  liquid  exceeds  that  of  the  same  quantity  of  vapor, 
i.  e.,  gas. 

A  similar  calculation  may  be  made  regarding  a  solid  or 
liquid  substance  and  its  solution  in,  e.  g.,  water,  in  which 
case  the  work  may  be  done  by  lifting  a  piston,  loaded 
per  cm.2  with  a  weight  equal  to  the  osmotic  pressure  of 
the  saturated  solution,  permeable  to  the  solvent  (water), 
but  not  to  the  dissolved  body,  and  separating  a  satu- 
rated solution  over  this  body  from  a  layer  of  pure  solvent. 

Of  course  all  these  deductions  regarding  the  free 
energy  A  are  based  upon  the  assumption  that  we  deal 
with  such  small  concentrations  that  the  laws  for  ideal 
gases  are  valid. 

Similar  expressions  referring  to  the  pressure  are  used 
for  gas-reactions  because  they  generally  take  place  at 
constant  pressure  and  because  the  pressure  is  generally 
the  quantity  observed.  The  same  expression  should 
be  used  for  solutions  if  their  condition  was  character- 
ized by  theb:  osmotic  pressure.  But  the  osmotic  pres- 
sure is  very  difficult  to  measure  and  instead  of  that 
we  use  the  concentration  c  in  defining  the  state  of  solu- 
tions. We  therefore  transform  the  equation  given 
above  by  introducing  in  the  expression  of  A  the  for- 
mula of  Boyle-Gay-Lussac : 

p  =  cRT.  (2) 

We  now  reckon  the  free  energy  from  a  certain  concen- 


198  THEORIES   OF   SOLUTIONS. 

tration  ca,  which  is  connected  to  pa  through  the  equa- 
tion: 

pa  =  caRT.  (2a) 

Introducing  the  said  values  of  p  and  pa  into  equation 
(1)  we  find: 

).  (3) 


If  we  put  ca  equal  to  the  unit  of  concentration  —  usually 
one  gram-molecule  per  liter,  we  get: 

A  =  RT  log,  c.  (3a) 

Let  us  consider  an  equilibrium  between  a  weak  acid, 
which  obeys  the  law  of  Guldberg  and  Waage,  and  its 
two  ions.  If  their  concentrations  are  Ci  and  02,  then 
the  so-called  dissociation  constant  is  K  =  of/Ci.  We 
wish  to  calculate  the  work  done  in  the  electrolytic  dis- 
sociation of  one  gram-molecule  of  the  acid  of  unit  con- 
centration into  its  two  ions  also  of  unit  concentration. 
For  this  calculation  we  make  use  of  the  circumstance 
that  an  equilibrium  exists  if  the  concentration  of  the 
acid  is  Ci  and  that  of  each  of  its  two  ions  GZ.  In 
other  words  no  work  is  done  if  we  transform  a  certain 
quantity  of  the  acid  of  the  concentration  Ci  into  its 
ions  when  their  concentration  is  c%  or  vice  versa.  Then 
the  work  to  be  calculated  consists  of  three  parts:  (1) 
The  work  done  in  the  dilution  of  one  gram-molecule  of 
the  acid  from  the  concentration  1  to  the  concentration  Ci 

A!  =  RT  (log,  1  -  log.  ci). 

(2)  The  work  done  in  transforming  the  said  mass  of 
the  acid  of  the  concentration  Ci  into  solutions  of  its 
two  ions,  each  of  the  concentration  c%  at  constant  vol- 
ume. This  work  is  zero.  (3)  The  work  of  condensing 


THE  DOCTRINE   OF  ENERGY.  199 

the  two  solutions  of  the  ions  from  the  concentration  Cz  to 
the  concentration  1  (the  original  volume).    This  work  is 


The  total  work  done  is: 
A  =  Ai  +  A3=  RT  (2  log.  02  -  log.  Ci)  =  RT  lo&K.  (4) 

As  K  is  generally  a  very  small  fraction,  A  is  generally 
negative,  i.  e.,  the  ions  possess  in  normal  solution  an 
excess  of  free  energy  above  that  of  the  acid  in  normal 
solution.  If  we  have  an  acid  in  double  the  normal  so- 
lution and  it  is  dissociated  into  its  ions  to  the  extent  of 
50  per  cent.  —  this  condition  is  nearly  realized  for  tri- 
chloracetic  acid  at  25°  —  then  the  free  energy  is  zero,  for 
an  equilibrium  exists  between  the  undissociated  acid 
and  its  two  ions,  all  three  in  normal  concentration,  so 
that  no  work  is  necessary  for  carrying  the  process  in  the 
one  or  the  other  direction.  In  this  case  the  dissocia- 
tion constant  is  1.  The  expression  above  is  due  to 
van't  Hoff. 

Evidently  it  is  very  easy  to  calculate  A,  if  we  know 
K,  and  van't  Hoff  did  that  with  the  help  of  the  deter- 
minations of  Ostwald.  He  found  for  instance  at  25°  C. 
for  acetic  acid  A  =  —  3,240,  for  formic  acid  A  =] 
—  2,510,  for  propionic  acid  A  =  —  3,320,  for  trichlor- 
acetic  A  =  +  60,  etc. 

The  free  energy  or  affinity  A  is  bound  to  the  quantity 
of  heat  U  developed  in  a  reaction  by  the  following 
equation,  which  is  easily  deduced  from  the  second  law 
of  thermodynamics: 

U-  A-TdA- 

U  "  A       i  dT  " 


200  THEORIES  OF   SOLUTIONS. 

If  we  know  A,  or  K  at  a  given  temperature  and  U  for 
all  temperatures,  then  we  may  calculate  K  for  any 
temperature  from  the  last  equation,  which  was  given 
by  van't  Hoff.  But  we  know  A  at  absolute  zero,  for 
there  according  to  the  last  equation  U  =  A.  Then 
knowing  U  we  may  determine  A. 

If  we  develop  A  in  a  series  in  the  neighborhood  of  0° 
absolute,  we  get 


We  need  only  two  terms  of  T  if  we  do  not  consider 
temperatures  too  far  from  0°  absolute.  Using  the  last 
equation  we  find  the  following  expression  for  U: 


This  equation  states  that  (dU:dT)  at  0°  absolute  is 
absolute  zero,  i.  e.y  U  does  not  change  with  temperature 
hi  the  neighborhood  of  absolute  zero.  This  seems  to  be 
nearly  true.  Einstein  has  recently  given  a  theory  ac- 
cording to  which  the  specific  heats  of  substances  vanish 
at  absolute  zero,  therefore  also  the  so-called  molecular 
heat,  i.  e.,  the  product  of  the  specific  heat  by  the  molec- 
ular weight  is  zero.  This  theory  has  lately  been  in 
a  high  degree  confirmed  by  the  measurements  of 
Schimpff  and  Pollitzer.  Now  the  change  of  U  with  tem- 
perature depends  on  the  difference  of  the  molecular 
heats  of  the  reacting  substances  on  the  two  sides  of 
the  sign  of  equality  in  the  chemical  equation  expressing 
the  reaction.  If  now  the  molecular  heats  are  zero, 
then  it  follows  that  their  differences  will  also  be  zero. 

The  determinations  of  Schimpff  and  Pollitzer  were 
carried  out  only  with  solid  substances.  The  said  regu- 


THE  DOCTRINE  OF  ENEEGY.  201 

larity  is  certainly  only  to  be  regarded  as  a  first  approxi- 
mation for  systems  in  which  gases  or  solutions  enter. 
A  has  a  maximum  (or  minimum)  when 

dA/dt  =  0  v  B  +  2CT  =  0, 
i.  e.,  at  an  absolute  temperature  T,  which  is 
T  =  -  B/2C. 

As  we  shall  see  this  temperature  is  positive,  i.  e.,  occurs, 
because  B  and  C  have  (hi  the  cases  examined  below) 
opposite  signs  (cfr.  fig.  5,  p.  212 ). 

At  the  same  temperature  At  and  Ut  are  equal,  for 
if  I  put 

At  =  A0  +  BT  +  CT*  =  Ut  =  A0-  CT\ 
I  find 

BT  =  -  2CT2,  i.  e.,T  =  -  B/2C. 

At  this  point  we  also  find: 

dU/dt  =  -  2CT  =  J5, 

i.  e.,  the  tangent  to  the  C7-curve  at  this  remarkable 
point  is  parallel  to  the  tangent  of  the  A-curve  at  the 
point  zero.  The  A-  and  Z7-curves  cut  each  other  at 
two  points,  at  T  =  0  and  at  T  =  -  B/2C.  In  the 
temperature  interval  between  these  two  points  they 
do  not  separate  much  from  each  other,  but  from  there 
they  diverge  more  and  more  rapidly  the  higher  the 
temperature  rises  according  to  the  prevalence  of  the 
term  CT*  in  A  above  BT.  In  U  the  term  -  CT2 
determines  the  variation,  which  goes  in  the  opposite 
direction  to  that  of  A. 

Other  interesting  points  are  those  in  which  At  and 
Ut  =  0.    For  Ut  =  0  we  have 

An  -  CT2  =  0  V  T..  =  i/ZTC 


202  THEORIES  OF  SOLUTIONS. 

and  for  At  =  0,  we  find 

A0  +  BT  +  CT*  =  0  v  Ta  =  -  B/2C 

The  examples  of  solutions  given  below  give  a  positive 
value  of  Tu  because  A0  and  C  are  of  the  same  sign. 
A  does  not  reach  zero  for  weak  electrolytes,  for  which 
it  may  be  calculated  with  sufficient  accuracy.  In 
order  to  elucidate  these  important  theorems,  I  have 
calculated  the  free  energy  of  two  solutions,  one  prac- 
tically not  dissociated,  namely  of  boric  acid,  and  the 
other  dissociated  to  a  high  degree.  The  figures  are 
taken  from  the  tables  of  Landolt-Bornstein,  third 
edition,  t  is  temperature  in  °C.,  T  absolute  tempera- 
ture, c  concentration  (gram  mol.  in  1000  gm.  H20). 

BORIC   ACID,   HjOsB  =  62. 

A  =  -7519+34.02T-0.025T2. 
t       T         e:2  logc:2         A  obs.        Alcaic.        Diff.       dAldt  U 

0  273  0.1562  -0.8064  -86-94+8  -5656 

20  293  0.3164  -0.4997  +  318    +  301     +17  20.2  -5372 

40  313  0.5523  -0.2579  +  686     +680     +6  18.4  -5071 

60  333  0.8352  -0.0679  +1019    +1037     -18  16.7  -4778 

80  353  1.288  0.1101  +1368     +1376     -  8  17.4  -4404 

100  373  2.062  0.3144  +1793     +1794     -  1  16.2  -4041 

dA/dt  is  nearly  constant  and  decreases  a  little  with 
increasing  temperature.  Thereby  C  receives  a  negative 
sign,  and  consequently  in  this  case  B  a  positive  one. 
A0  is  negative.  These  signs  of  A0,  B  and  C  are,  as 
we  shall  see  later,  those  generally  found.  Where 
A0,  B  and  C  do  not  come  out  with  these  signs  we  may 
suspect  that  the  observations  are  affected  by  some 
rather  great  errors  (or  the  temperature  interval  is  insuf- 
ficient for  determining  A0,  B  and  C  with  accuracy).  As 
U  =  A0  —  CT2,  the  numerical  value  of  U  decreases 


THE  DOCTRINE  OF  ENERGY. 


203 


with  rising  temperature.  That  B  is  positive  depends 
upon  the  fact  that  the  solubility  always  increases  at 
low  temperatures.  The  solubility  is,  according  to  the 
negative  sign  of  A0,  as  we  shall  see  below  always 
vanishing  in  the  neighborhood  of  absolute  zero.  The 
change  of  A  and  U  with  temperature  is  given  for 
H303B,  Ca(OH)2  and  (C2H5)20  in  the  accompanying 
diagram. 


[•¥10000 


1*5000  fisiffil! 


+300 


S^rigPZrisiift. 


100        200 

FIG.  4. 


30O      400 


We  now  take  a  very  interesting  example,  in  which 
U  is  positive  at  common  temperature,  i.  e.,  in  which 
heat  is  developed  on  solution,  namely  the  solubility 
of  Ca(OH)2. 

CALCIUM  HYDRATE  Ca  (OH)8=74. 

t      T         C  logc         TTobs.     TPcalc.     Diff.    dWIdt         U          U.2.62 

0  273  0.0234  0.3691-2  -1910  -1885  -25   —  +  627  +  1643 

40  313  0.01856  0.2688-2  -2331  -2332  +  1-9.6  +1799  +  4714 

80  353  0.01196  0.0779-2  -2938  -2942  +  4  -14.3  +3130  +  8200 

150  423  0.00446  0.6497-3  -4356  -4380  +24  -19.1  +5845  +15314 

RT  log,  c  =  W  =  -3100  +  18.17  -  0.05T2. 

As  in  the  example  given  above  the  formula  with  three 
constants  represents  the  observations  surprisingly  well, 


204  THEORIES  OF  SOLUTIONS. 

and  within  the  limits  of  experimental  errors.  Just  as 
in  the  previous  case  A0  is  negative,  i.  e.,  the  substance 
is  absolutely  insoluble  at  extremely  low  temperatures — 
which  in  reality  are  not  accessible  for  experiments.  B  is 
positive,  i.  e.,  the  solubility  increases  to  begin  with, 
which  is  a  necessary  consequence  of  what  has  been  said 
regarding  the  insolubility  at  0°  abs.,  and  C  is  negative, 
i.  e.,  the  numerical  value  of  the  heat  of  solution  (if 
negative  as  hi  normal  cases)  decreases  with  rising  tem- 
perature (or  increases  if  positive  as  for  Ca(OH)2). 
As  A0  and  C  always  have  the  same  sign  U  is  zero  at  a 
certain  temperature;  in  the  two  examples  given  above 
this  point  lies  at  548°  abs.  (=  275°  C.)  for  boric  acid 
and  at  249°  abs.  (=  -  24°  C.)  for  Ca(OH)2.  The 
point  at  which  A  has  its  maximum  value  and  is  equal 
to  U  lies  for  boric  acid  at  680°  abs.  (=  407°  C.)  and 
for  calcium  hydrate  at  220°  abs.  (=  -  53°  C.).  These 
temperatures  are  inaccessible  experimentally  as  well  for 
the  calcium  hydrate  as  for  the  boric  acid. 

The  calcium  hydrate  hi  saturated  solution  is  disso- 
ciated electrolytically  to  a  degree  of  81  per  cent.  There- 
fore its  osmotic  pressure  is  2.62  tunes  greater  than  if 
the  molecules  were  simple.  In  order  to  correct  for 
this  peculiarity  van't  Hoff  introduced  the  coefficient  i, 
so  that  the  constant  R  has  2.62  times  greater  value  than 
for  gases  and  undissociated  substances.  Hence  also 
the  A  and  U  should  be  multiplied  by  this  factor.  If 
this  is  done  we  find  at  18°  C.,  the  heat  of  solution 
(IT)  equal  to  2,930,  whereas  Thomsen  found  experi- 
mentally 2,800,  a  very  good  agreement.  For  boric  acid 
Berthelot  found  -17=  5,600,  whereas  the  calculation 
above  gives  —5,400,  which  is  also  in  good  agreement 
within  the  experimental  errors. 


THE   DOCTRINE   OF  ENERGY. 


205 


I  have  found  only  a  single  class  of  dissolved  sub- 
stances, for  which  the  rule  that  A0  and  C  are  negative 
and  B  positive  does  not  hold.  This  class  is  fluids, 
which  are  only  partially  immiscible  with  water.  As 
these  substances  are  also  highly  interesting  from  other 
points  of  view,  I  have  calculated  three  typical  exam- 
ples, namely  ethyl  ether,  2-4-6  trimethyl  pyridine  and 
phenol.  For  ether  the  solubility  in  the  investigated 
interval  decreases  with  rising  temperature,  for  phenol 
it  increases  steadily  and  for  trimethylpyridine  it  at 
first  decreases  and  thereafter  increases.  The  solubility 
c  is  given  in  gram-molecules  per  kilogram. 


ETHYL  ETHER,  C2H6OC2H5  =  74  (KLOBBIE). 


t  T          e 

-  3.5  269.5    1.63 

+20  293 

40  313 

60  333 

80 


Iog10c 


dWldi 


0.2123 


17 

+4812 


W  obs.  W  calc.     Diff. 

262  260    +     2 

0.857    0.9329-1    -  90  -  90           0  -15.0     +3756 

0.597    0.7762-1    -320  -321    +     1  -11.5     +2787 

0.48     0.6810-1    -485  -483    -     2  -  8.3     +1753 

353      0.368    0.5667-1    -699  -587    -112  -10.7?  +  653 
W=  RT  loga  c  =  10,623  -  60T  +  0.08T2. 

2-4-6  TRIMETHYL  PYRIDINE,  (CH3)3  C6H2N  =  121  (ROTHMTTND).    Crit. 

Point  5.7°. 
c  log10c 


t  T 

10  283  0.6404  0.8065-1 

20  293  0.2819  0.4500-1 

40  313  0.1593  0.2021-1 

80  353  0.1428  0.1547-1 

120  393  0.1537  0.1866-1 


IT  obs.      TFcalc.        Diff.  dWldt            U 

-  250  -  607  +357  —  +3746 

-  737  -  753  +  16  -48.6  +3342 
-1141  -1104  -137  -20.2  +2495 

-  25  -  5.6  +  628 

-  11 


-1364 
-1461 


-1349 
-1450 


-  2.5  -1461 


160  433  0.2417  0.3832-1  -1221  -1339  +118  +  6.0  -3772 

180  453  0.3024  0.4806-1  -1075  -1098  +  23  +  7.3  -5013 

W  =  RT  log,  c=  9,352  -  55T  +  0.07T2. 

PHENOL,  C6H6OH  =  74  (ROTHMUND).    Crit.  Point  68.8°. 

t  T          e  Iogi0c 

0  273  0.761  0.8816-1 

20  293  0.898  0.9534-1 

40  313  1.044  0.0188 

50  323  1.296  0.1125 

60  333  1.828  0.2644 

65  338  2.402  0.3805 


W 


TPobs.  TFcalc.         Diff.  dWldt              U 

-148.3  +174  -322.3         +  5508 

-  62.1  -  71  -  11.1  +  4.3  +    983 

+  26.9  +  16  +  10.9  +  4.5  -  3859 

+171.2  +190  -  18.8  +14.4  -  6408 

+426.5  +424  +    2.5  +25.5  -  9022 

+622.4  +584  +  48.4  +39.2  -10572 
RT  log.  c=35,328-238T+0.4T2. 


206  THEORIES  OF  SOLUTIONS. 

The  points  for  which  U  is  zero  are  364°  absolute 
(91°  C.)  for  ether,  365.5  (92.5°  C.)  for  trimethylpyri- 
dine,  which  also  results  from  the  minimum  of  c  at  that 
point,  and  299.1  (=  26.5°  C.)  for  phenol.  This  last 
point  does  not  agree  with  the  observations,  for  nothing 
indicates  a  minimum  of  c  at  that  point,  but  as  we  see, 
we  cannot  speak  of  an  agreement  between  the  calcu- 
lation and  observation  below  20°  C.  The  same  is  true 
for  the  temperature  above  60°  for  ether  (perhaps  this  is 
partly  due  to  errors  of  observation)  and  below  20°  C. 
for  the  trimethylpyridine.  The  point,  where  A  —  W 
+  2T  has  its  minimum  value  and  A  =  U  falls  at  362° 
(=  89°  C.),  379°  (106°  C.)  and  295  (=  22°  C.)  for  the 
three  substances.  This  point  is  clearly  visible  for  tri- 
methylpyridine and  for  phenol.  For  ether  this  point  lies 
above  the  temperatures  examined.  U  is  for  ether  4,500 
cal.  at  common  temperature  according  to  an  observation 
by  Le  Chatelier.  The  agreement  is  satisfactory.  It  is 
evident  that  the  ground  for  the  abnormal  behavior  of 
these  substances  lies  in  the  very  great  positive  value  of  C, 
i.  e.,  d?A/dP  in  the  examined  interval  of  temperature. 
As  is  seen  from  the  figures  of  dA/dt,  d2A/dt2  is  by  no 
means  constant  in  this  interval,  and  it  is  therefore  not  to 
be  expected  that  a  constant  value  of  C  will  allow  an  ex- 
trapolation. This  is  exceedingly  clear  for  phenol,  and 
the  observations  regarding  the  other  two  substances 
leave  no  doubt  that  an  extrapolation  with  a  constant 
value  of  C  cannot  give  reliable  results.  These  obser- 
vations fall  in  the  neighborhood  of  the  critical  points 
of  these  mixtures  and  it  is  well  known  that  the  simpli- 
fied formulae  of  van't  Hoff,  in  which  the  volume  of  the 
fluid  is  omitted  are  not  applicable  in  the  neighborhood 


THE  DOCTRINE  OF  ENERGY.  207 

of  the  critical  point.  We  shall  later  see  this  assertion 
exemplified.  Hence  we  ought  not  to  draw  conclusions 
regarding  the  values  of  A0,  B  and  C  for  these  substances 
from  the  formulae  given  above,  which  are  only  inter- 
polation formulae.  The  great  value  of  C  causes  an 
abnormally  high  negative  value  of  B  and  this  in  its 
order  gives  rise  to  the  wholly  abnormal  positive  value 
of  A0.  But  still  one  regularity  remains,  namely  that 
A0  and  C  are  of  the  same  sign  and  opposite  to  that  of  B. 
In  other  words  U  passes  through  zero  at  some  point 
and  the  U-  and  A  -curves  intersect  at  some  point  (above 
absolute  zero).  But  we  should  not  draw  any  conclu- 
sions regarding  the  real  values  of  A0,  B  and  C  from  these 
experiments. 

Van't  Hoff  has  determined  a  great  number  of  heats 
of  solution  from  observations  regarding  solubility  and 
compared  them  with  observed  data.  This  list  of  sub- 
stances is  the  following  (U  expressed  in  great  calories): 


Stance.  So.uWH*  ,n  PM  C.n, 

Succinic  acid  .....  2.88  at    0°,  4.22  at    8.5°  6.7  6.9 

Salicylic  acid  .....  0.16  at  12.5,  2.44  at  81  8.5  8.0 

Bcnzoic  acid  .....  0.182  at    4.5,  2.19  at  75  6.5  6.8 

Amyl  alcohol  .....  4.23  at    0,  2.99  at  18  —2.8  —3.0 

Anilin  ..........   3.11  at  16,  3.58  at  55  0.1  0.7 

Phenol  ..........  7.12  at    1,  10.2    at  45  2.1  1.4 

Mannite  .........  15.8  at  17.5,  18.5    at  23  4.6  4.9 

Mercuric  chloride.   6.57  at  10,  11.84  at  50  3.0  2.7 

Boric  acid  .......   1.95  at    0,  2.92  at  12  5.6  5.2 

Van't  Hoff  also  introduced  for  these  substances, 
which  are  nearly  perfect  non-conductors,  a  magnitude 
i,  similar  to  that  spoken  of  above  for  calcium  hydrate. 
As  this  magnitude  i  depends  upon  the  dissociation  of 
the  substances, 

i  =  1  +  (n  -  IK 


208  THEORIES  OF  SOLUTIONS. 

where  n  is  the  number  of  ions,  into  which  the  electro- 
lyte dissociates  and  a  is  the  degree  of  dissociation,  and 
a  in  all  these  cases  is  practically  equal  to  zero,  I  have 
recalculated  the  figures,  putting  i  =  1.  In  reality 
they  have  not  changed  much. 

Van't  Hoff  has  also  given  figures  for  some  electro- 
lytes which  are  dissociated  to  such  a  degree  that  we 
must  take  i  as  greater  than  unity,  as  for  Ca(OH)2  above. 
The  influence  of  the  dissociation  is  easily  understood  in 
the  case  of  gases.  If  the  gas  does  consist  of  just  the 
simple  molecules,  indicated  by  its  chemical  formula, 
we  may  substitute  RT.c  for  p  where  c  is  the  concentra- 
tion. But  if  every  one  of  the  molecules,  represented 
by  the  formula,  is  split  up  into  i  molecules  (ions)  then 
the  pressure  is  i  times  greater  than  that  calculated 
from  the  formula  p  =  RTc.  It  is  easy  to  see  from  the 
deduction  of  the  formula  above,  that  the  same  is  valid 
also  for  solutions,  namely  that  we  must  multiply  c  by 
i,  in  order  to  get  correct  values.  That  is  what  we  have 
done  above  for^calcium  hydrate,  in  which  case  i  may 
be  taken  as  a  constant.  But  in  other  cases,  especially 
where  the  solubility  increases  with  temperature,  as  in 
normal  instances  this  is  not  permissible  but  we  ought 
to  tabulate  A  =  iRT  (1  -f  log,  ic). 

Van't  Hoff  supposed  that  i  is  constant  and  found  a 
good  agreement  between  the  observed  and  the  calcu- 
lated figures.  Probably  a  revision  of  the  figures  will 
also  verify  the  ideas  of  van't  Hoff;  at  present  it  may 
suffice  to  indicate,  how  the  recalculation  has  to  be 
performed.  I  reproduce  only  some  few  figures  calcu- 
lated by  Noyes,  regarding  silver  salts,  showing  an 
excellent  agreement  with  the  figures  observed  by 
Goldschmidt. 


THE  DOCTRINE  OF  ENERGY.  209 

Salt.  AgC.H.O,  AgC3HsOt  AfC4HTO, 

Heat  of  solution  obs 4,613  3,980  2,860 

Heat  of  solution  calc. . .  4,562  3,928  2,836 

I  now  come  to  the  most  interesting  case  regarding 
the  energy  of  solutions,  namely  the  change  of  free 
energy  on  electrolytic  dissociation  and  the  simultaneous 
evolution  of  heat.  We  shall  see  that  the  circumstances 
are  very  similar  to  those  observed  in  the  solution  of 
substances. 

We  begin  with  examining  some  substances  which 
have  been  accurately  investigated  in  a  rather  great 
interval  of  temperature,  and  thereafter  consider  other 
substances,  which  have  not  been  measured  so  thor- 
oughly. 

In  his  great  Carnegie-Institute  memoir,  which  I  have 
so  often  cited,  Noyes  gives  some  figures  for  the  dis- 
sociation constants  of  water,  acetic  acid,  ammonia  and 
phosphoric  acid,  at  different  temperatures  in  a  rather 
great  interval,  so  that  they  may  well  serve  as  instructive 
examples  of  the  variation  of  affinity  of  electrolytes. 

The  interpolation  formulae  used  for  representing  the 
A -values  are  for 

Water;  H  +  OH  =  H20;  A  =  21420  +  29.91T  - 
0.085772. 

Acetic  acid;  H  +  CH3C02  =  CH3C02H;  A  =  -  5360 
+  14.66T  -  0.0615772. 

Ammonia;  NH4  +  OH  =  aNH4OH  +  (1  -  a)  (NH3  + 
H20);  A  =  -  8625^+  32.63T7  -  0.0851772. 

Phosphoric  acid;  H  +  H2P04  =  H3P04;  A  =  -  1955 
+  11.977  -  0.0446T2. 

It  is  interesting  to  see  how  well  these  interpolation 
formulae  represent  the  observations.    I  therefore  give 

15 


210 


THEORIES  OF  SOLUTIONS. 


below  the  observed  and  the  calculated  values  of  A. 
The  next  column  contains  the  difference  Aobs,  -  ACQic. 
After  this  the  value  of  dA/dt  calculated  from  ^Obs.  is 
tabulated.  7  gives  the  temperature  hi  °C.,  T  is  the 
absolute  temperature. 


WATER. 

t 

T 

A  obs. 

A  calc. 

Diff. 

—dAldt 

0 

273 

-18780 

-18795 

+  15 



18 

291 

-19070 

-19064 

-  6 

16.1 

25 

298 

-19190 

-19181 

-  9 

17.1 

100 

373 

-21000 

-21010 

+  10 

24.1 

156 

429 

-22850 

-22987 

+137 

33.04 

218 

491 

-25440 

-25783 

+343 

41.77 

306 

579 

-31160 

-30801 

-359 

65.00 

ACETIC  ACID. 

t 

T 

^1  obs. 

A  calc. 

Diff. 

—  dAldt 

IS 

291 

-  6306 

-  6300 

-  6 



100 

373 

-  8446 

-  8446 

0 

26.1 

156 

429 

-10330 

-10391 

+  61 

33.7 

218 

491 

-12940 

-12990 

+  50 

42.0 

306 

579 

-18150 

-17486 

-664 

59.2 

AMMONIA. 

t 

:  T 

A  obs. 

A  calc. 

Diff. 

—  dAldt 

0 

273 

-  6058 

-  6056 

-  2 



18 

291 

-  6337 

-  6331 

-  6 

15.5 

25 

298 

-  6463 

-  6456 

-  7 

18.6 

50 

323 

-  7002 

-  6962 

-  40 

21.6 

75 

348 

-  7612 

-  7573 

-  39 

24.4 

100 

373 

-  8302 

-  8284 

-  18 

27.6 

128 

401 

-  9066 

-  9217 

+151 

27.3 

156 

429 

-10202 

-10283 

+  81 

41.3 

218 

491 

-12894 

-13113 

+219 

43.4 

306 

579 

-18610 

-18147 

-463 

64.9 

PHOSPHORIC  ACID. 

t 

T 

A  obs. 

A  calc. 

Diff. 

—  dAldt 

18 

291 

-  2638 

2629 

-  9 



25 

298 

-  2761 

2749 

-12 

17.6 

50 

323 

-  3181 

3178 

-  3 

16.8 

75 

348 

-  3689 

3665 

-24 

20.3 

100 

373 

-  4208 

4203 

-  5 

20.8 

128 

401 

-  4860 

4876 

+16 

23.3 

156 

429 

-  5585 

5623 

+38 

25.9 

THE  DOCTKINE  OF  ENERGY.  211 

The  temperature  interval  is  not  so  very  great  for  the 
observations  on  H3P04;  therefore  this  example  is  of 
much  less  value  than  the  other  series.  At  high  tem- 
peratures the  differences  between  the  observed  and 
calculated  values  increase,  which  may  perhaps  be  due 
to  the  difficulty  of  these  observations,  perhaps  also  to 
the  circumstance  that  the  higher  members  in  the  inter- 
polation formula  have  been  omitted  and  probably  to 
both  of  these  circumstances.  The  great  negative  values 
of  these  differences  at  T  =  306,  compared  with  the 
positive  values  at  the  nearest  temperatures  T  =  156 
and  T  =  218,  indicate  that  the  coefficient  D  of  the 
omitted  term  DT3  is  negative,  i.  e.,  of  the  same  sign  as 
C.  From  this  it  also  follows  that  the  numerical  value 
of  C  given  above  is  a  little  too  high. 

All  the  four  interpolation  formulae  are  of  the  same 
type,  the  values  of  A0  and  of  C  are  all  negative,  the  B 
values  are  positive.  Very  remarkable  is  the  circum- 
stance that  whereas  the  four  values  of  A0  are  rather  dif- 
ferent (in  the  proportion  11  to  1),  the  values  of  B  do  not 
change  so  much  (only  in  the  proportion  2.8  to  1)  and 
still  less  is  the  variability  of  C  (only  as  1.9  to  1). 

The  characteristic  point,  where  A  has  its  maximum 
value,  and  where  the  A-  and  {/-curves  intersect,  lies  at 
the  following  absolute  temperatures  (at  double  this 
temperature  A  has  the  same  value  as  at  T  =  0) : 

for  H20;  T  =  176  (t  =  -  97°  C.) 

for  CH3C02H;  T  =  119  (t  =  -  154°  C.) 
for  NH3;  T  =  192  (t  =  -  81°  C.) 

for  H3P04;  T  =  134  (t  =  -  139°  C.) 

i.  e.9  about  150  to  80  degrees  below  the  freezing  point 

of  water. 


212 


THEORIES   OF   SOLUTIONS. 


The  other  characteristic  point,  where  U  =  0,  and 
consequently  the  dissociation  is  at  its  maximum,  lies: 

for  H20  at  T  =  502  (t  =  229) 

for  CH3C02H  at  T  =  295  (t  =    22) 
for  NH3  at  T  =  318  (t  =    45) 

for  HsP04        at  T  =  209  (t  =  -  64) 

It  is  easy  to  calculate  the  heat  of  dissociation  from 
the  variation  of  K  with  temperature.  In  drawing  a 
curve  through  the  points  representing  U  as  a  function 
of  temperature  it  is  easy  to  find  the  temperature,  where 
U  =  0.  This  point  will  of  course  agree  with  that 
calculated  above  and  I  actually  find  from  the  curves 
the  values  Tu  =  502  for  water  Tu  =  295  for  acetic  acid 
and  Tu  =  318  for  ammonia.  The  zero  point  of  U  for 
HsPCX  lies  64  degrees  below  zero  of  the  thermometric 
scale  and  is  therefore  not  accessible  experimentally. 


l-JQOOO 


400 


600 


FIG.  5. 


The  great  value  of  these  observations  depends  upon 
their  proximity  to  the  zero  of  absolute  temperature. 


THE  DOCTRINE  OF  ENERGY. 


213 


The  interval  of  observed  temperatures  is  about  as  great 
as  that  below  0°  C.  It  is  therefore  probable  that  the 
formulae  will  give  nearly  right  results  also  below  0°  C.  and 
down  to  the  neighborhood  of  absolute  zero.  I  have 
given  a  graphic  representment  of  the  formulae  for  water 
hi  the  accompanying  curves  and  in  these  I  have  also 
introduced  the  values  of  U  calculated  directly  from 
Noyes'  figures.  If  the  [/-curve  had  not  a  horizontal 
tangent  at  T  =  0,  the  value  of  dA/dt  would  have  an 
infinite  value  at  the  same  temperature.  In  other 
words,  the  A  curve  ought  there  to  run  vertically  and 
make  an  extremely  sharp  bend.  This  is  not  probable 
although  not  quite  impossible. 


1*15000 


J+WOVO 


tsooo 


-•  £000 


»JOOOO 


ZOO        400 
FIG.  6. 


600 


There  are  very  few  cases  in  which  the  A  values  are  so 
accurately  determined  so  near  to  the  absolute  zero  and 
within  so  great  an  interval  as  just  these.  Only  the  A 


214  THEORIES  OF  SOLUTIONS. 

values  for  transformation  of  vapor  into  water  may 
compare  with  them,  and  to  which  I  therefore  wish  to 
refer  for  a  comparison.  Here  A  =  RT  (1  +  log,  p).  Of 
course  the  value  of  A  depends  on  the  units  hi  which  p 
is  expressed,  for  instance,  millimeters  of  mercury  or  at- 
mospheres. If,  as  generally  done,  p  is  given  in  milli- 
meters, which  unit  I  also  use  below,  then  A  expresses 
the  maximal  work  obtained  in  transforming  steam  at 
1  millimeter  pressure  to  water  in  a  reversible  way  and 
at  constant  temperature. 


t 

FLUID  WATER  —  »  WATEB  VAPOR. 
W  =  RT  log,  p  =  -  11394  +  46.74T  -  0.00927T2. 

T              p  obs.             p  calc.             W  obs.            W  calc  .         Diff- 

dWIdt 

-20 

253 

0.96 

1.00 

-       25 

-        12 

-  13 



0 

273 

4.579 

4.58 

+      825 

+     825 

-     0 

42.5 

50 

323 

92.17 

90.6 

+  2,901 

+  2,887 

+  14 

41.5 

100 

373 

760 

760.3 

+  4,911 

+  4,909 

+    2 

40.2 

150 

423 

3,581 

3,581 

+  6,870 

+  6,869 

+     1 

39.2 

200 

473 

11,625 

11,639 

+  8,788 

+  8,789 

-     1 

38.4 

250 

523 

29,843 

29,101 

+10,695 

+10,665 

+  30 

38.1 

300 

573 

67,620 

59,020 

+12,650 

+12,495 

+155 

39.1 

350 

623 

126,924 

90,440 

+14,550 

+14,127 

+323 

37.9 

As  is  seen  from  these  figures  the  agreement  is  excellent 
at  0, 100,  150  and  200°,  and  sufficient  at  -  20,  50  and 
250°.  At  higher  temperatures  the  difference  between 
observed  and  calculated  values  increases  rapidly.  This 
peculiarity  is  evidently  due  to  the  omission  of  a  term 
DT3,  where  D  has  a  positive  sign.  The  proximity  of 
the  critical  point  (365°  C.)  is  without  doubt  the  cause 
of  these  irregularities  (cf.  p.  207).  The  attempt  to 
give  the  formula  without  D  a  so  great  interval  of 
validity  as  possible  has  brought  about  that  the  effect 
of  D  has  partially  been  attributed  to  C  which  therefore 
is  a  little  greater  than  in  reality.  To  compensate  for 


THE  DOCTRINE  OF  ENERGY.  215 

this  at  low  temperatures,  £,  which  is  of  opposite  sign 
to  Cj  has  also  been  taken  a  little  too  small  and  that 
has  again  caused  a  value  of  A0,  which  is  a  little  greater 
than  in  reality.  Yet  the  error  in  A 0  is  probably  not 
greater  than  about  180  calories,  i.  e.,  without  appreci- 
able importance.  Differences  of  this  order  of  magni- 
tude may  also  be  possible  in  the  values  of  AQ  for  the 
dissociation  of  electrolytes,  but  the  errors  in  B/C  and 
A0fC  are  probably  still  less,  so  that  an  appreciable 
deformation  of  the  curves  is  excluded. 

It  is  noteworthy  that  if  we  designate  p  in  another 
unit,  e.  g.,  1,000  mm.  Hg,  then  RT  log,  p  decreases 
with  RT  log.  M/m  where  M/m  is  the  ratio  of  the  new 
and  the  old  unit,  i.  e.,  here  1,000.  The  decrease  of  A 
would  then  in  this  case  be  1.985.T.2.3026  log.  M/m  = 
13.71  T.  In  order  to  abolish  the  term  48.74T7  in  the 
expression  for  A  it  would  therefore  suffice  to  designate 
the  pressure  in  a  unit  which  is  1000™,  where  m  = 
48.74  : 13.71  =  3.555,  i.  e.,  4.62.1010  times  greater  than 
1  mm.  Hg.  Of  course  this  unit  is  of  no  practical 
value,  at  least  at  present. 

A  similar  remark  may  be  made  regarding  the  dis- 
sociation constant  of  the  electrolytes.  If  I  use  a  unit, 
which  perhaps  is  more  consistent  with  the  absolute 
system  C.G.S.  than  the  gram-molecule  per  liter,  namely, 
the  gram-molecule  per  cubic  centimeter,  all  the  values  of 
K  diminish  in  the  proportion  1,000  to  1.  Therefore 
A  decreases  by  13.71  T7.,  i.  e.,  the  coefficient  B  decreases 
in  its  absolute  value  by  13.71.  The  magnitude  of  the 
coefficient  B  is  here  not  so  great  as  for  the  evaporation 
of  water,  therefore  it  is  not  necessary  to  change  the 
units  so  much  to  get  rid  of  the  term  BT.  As  units  of 
volume  should  be  taken  instead  of  liter 


216  THEORIES  OF  SOLUTIONS. 

for  ammonia  0.0725  cubic  millimeter, 
for  acetic  acid  0.617  cubic  millimeter, 
for  phosporic  acid  2.5  cubic  millimeter. 

Instead  of  increasing  the  unit  of  volume  in  the  said 
proportion  we  may  diminish  the  unit  of  mass  in  the 
same  proportion  with  the  same  result. 

It  is  very  easy  to  construct  the  curves  thus  trans- 
formed. It  is  only  necessary  to  draw  the  tangent  of 
the  A  -curve  at  the  point  T  =  0  and  to  count  the  A- 
values  from  an  axis  going  through  the  origin  parallel 
to  this  tangent.  Then  the  formulae  for  A  and  U  are 

A  =  Ao  +  CT2  +  DT*  +  ET*  +  .  .  ., 
U  =  AQ  -  CT2  -  2DT3  -  SET* .  .  .. 

At  low  values  of  T  we  may  omit  the  higher  terms  in- 
cluding T3  and  T4  and  then  the  condition,  demanded  by 
Nernst  for  condensed  systems,  namely,  that  the  A- 
and  17-curves  shall  be  related  to  each  other  as  object 
and  image  in  a  mirror  is  true.  But  as  soon  as  the 
higher  terms  T3,  etc.,  can  no  longer  be  neglected,  which 
happens  in  the  cases  investigated  above,  at  tempera- 
tures above  150  to  250  degrees,  then  the  similarity  of 
the  two  curves  is  spoiled. 

There  is  no  better  proof  of  the  small  physical  impor- 
tance of  the  coefficient  B  than  that  it  may  be  reduced  to 
zero  or  given  any  value  by  changing  the  units  of  meas- 
urement. Therefore  it  is  clear  that  an  assertion  that  B 
is  zero  at  the  absolute  zero  would  have  very  little  mean- 
ing in  this  case.  The  case  is  somewhat  different  if  in  the 
homogeneous  equilibrium  between  gases  or  dissolved 
substances  the  number  of  molecules  does  not  change 
through  the  transformation  or  if  we  work  with  pure 
substances  as  in  studying  the  dissociation  of  water  or, 


THE  DOCTRINE  OF  ENERGY.  217 

better  said,  with  substances  the  concentration  of  which 
cannot  be  changed  at  constant  temperature.  But  even 
in  this  case  as  we  have  seen  above  with  water,  there  is 
no  probability  that  the  A  -curve  runs  horizontally  at 
T  =  0,  although  special  cases  may  agree  rather  well 
with  this  condition.  This  seems,  for  instance,  to  occur 
with  some  condensed  systems,  for  instance  with  the 
transformation  of  rhombic  sulphur  into  monoclinic  as 
studied  by  Broensted.  AQ  and  C  are  not  dependent  on 
the  adopted  unit  of  pressure  or  concentration;  the  same 
is  evidently  the  case  with  U. 

The  formula  for  the  free  energy  A  on  transforming 
water  vapor  at  1  millimeter  pressure  into  fluid  water 
has  the  same  form  as  the  formulae  for  the  free  energy 
on  transforming  ions  of  normal  concentration  into  un- 
dissociated  substances  of  the  same  concentration.  But 
the  constants  are  very  different,  so  that  the  temperature 
where  A  has  its  maximum  value  occurs  at  first  at  2,520° 
absolute,  where  of  course  these  simplified  calculations 
have  no  real  meaning.  Even  the  temperature  where 
U  vanishes  is  very  high,  it  is  calculated  to  836°  C. 
The  said  temperature  occurs  much  sooner  because  of 
the  positive  value  of  D.  As  a  matter  of  fact  U  is  zero 
at  the  critical  point  638°  abs.  On  evaporation  A  goes 
through  zero  just  at  the  point  where  the  vapor 
pressure  is  equal  to  the  arbitrarily  chosen  unit  (here  it 
is  1  millimeter  and  this  pressure  is  valid  at  about — 20°C. ; 
if  we  had  chosen  1  atmosphere  A  would  have  passed 
through  zero  at  exactly  100°  C.).  An  inspection  of  the 
curves  giving  A  and  U  as  functions  of  T  shows  that  in 
the  case  of  evaporation  the  part  of  the  curves  between 
0°  and  600°  abs.  corresponds  only  to  the  part  of  the  A- 


218  THEOEIES  OF  SOLUTIONS. 

and  U-  curves  for  electrolytic  dissociation,  which  lie 
between  about  0°  and  40°  abs. 
By  differentiation  we  find  : 

dA  dU     B  +  2CT          /.        B 


dt  '  dt         -  2CT 


/.   ,         \ 

"\     1"2CT/' 


If  we  know  dA/dt  and  dU/dt  at  a  given  temperature 
(not  too  high),  we  may  easily  calculate  —  B  :  2C,  which 
is  the  temperature  where  A  has  its  maximum  (or 
minimum)  value  and  the  U-  and  A-curves  intersect. 
In  his  inaugural  dissertation  Lund6n  has  calculated  all 
available  values  of  dA/dt  and  dU/dt  at  25°  C.  =  298° 
abs.  With  the  aid  of  his  table  we  calculate  the  follow- 
ing values  Tm  of  the  absolute  temperature  of  Amax. 
298°  absolute  does  not  lie  very  high,  so  that  probably 
the  errors  hi  the  value  of  this  temperature  Tm  are  not 
so  very  great,  perhaps  some  30°  C.  Lunden  also  gives 
the  values  of  A  and  U  at  25°;  it  is  rather  interesting  to 
see  how  far  they  have  diverged  from  each  other  from 
the  point  of  equality  Tm.  With  Lunden,  I  have  divided 
the  material  into  three  groups.  The  first  contains 
bases,  the  second  acids,  which  dissociate  with  absorp- 
tion of  heat,  and  the  third  those  with  production  of  heat 
at  25°  C.  Through  the  subtraction  of  the  heat  of  disso- 
ciation of  a  weak  acid  from  that  of  water  we  obtain  the 
heat  of  neutralization  of  this  acid  with  a  strong  base. 
In  an  analogous  manner  the  heat  of  neutralization  of  a 
weak  base  with  a  strong  acid  is  obtained  and  also  the 
change  of  free  energy  on  neutralizing  the  said  sub- 
stances. In  the  neutralization  of  weak  acids  with  weak 
bases  it  is  necessary  to  take  the  A  and  U  values  for  both 
substances  into  consideration.  In  Lund£n's  work  these 


THE  DOCTRINE   OF  ENERGY. 


219 


neutralization  data  are  tabulated, 
essary  to  reproduce  them. 


I  do  not  find  it  nec- 


FREE  ENERGY  AND  HEAT  IN 


IONIZATION  PROCESSES  AT  25°  C. 

A  U  dAldt          dUldt 


Water  

-21,450 

-13,450 

-27 

+  50 

Bases: 

Orthoaminobenzoic  acid 

-16,220 

-10,220 

-21 

+  52 

Pyridine  

....-11,840 

-  7,780 

-13.5 

+  35.5 

2,  4,  6  Trimethyl  pyridine  . 

....  -  9,110 

-  5,510 

-12 

+  77 

Ammonia  

....-  6,440 

-  1,160 

-17.5 

+  58 

Acids  with  negative  heat  of 

diss.  : 

. 

Boric  acid  

....-12,570 

-  2,960 

-32 

+  12 

p-Nitrophenol  

-  9,750 

-  4,840 

-16.5 

+  21 

Orthoaminobenzoic  acid  .  .  . 

....  -  6,780 

-  3,270 

-12 

+  38 

Aminotetrazol  

-  8,420 

-  4,600 

-13 

+  55 

Cinnamic  acid  

....  -  6,070 

-      400 

-19 

+  31 

Benzoic  acid  

....-  5,690 

-     200 

-18.5 

+  42 

Nitrourea  (at  20°)  

....-  5,600 

-  3,700 

-  6 

+100 

m-oxybenzoic  acid  

....-  5,560 

-      100 

-18.5 

+  26 

m-nitrobenzoic  acid  

....-  4,720 

-      400 

-14.5 

+  38 

Nitro-urethane  

....-  4,470 

-  2,900 

-  5 

+  65 

Salicylic  acid  

....-  4,060 

-      800 

-11 

+  44 

Acids  with  positive  heat  of  c 

lias.:    • 

Acetic  acid  

....  -  6,450 

+      110 

-22 

+  31.5 

Ortho  toluylic  acid  

....-  5,320 

+  1,310 

-22 

+  30 

Ortho  chlorbenzoic  acid 

....  -  3,920 

+  2,240 

-20.5 

+  35 

Ortho  iodbenzoic  acid  

....  -  3,900 

+  2,660 

-22 

+  23 

Ortho  nitrobenzoic  acid 

....  -  3,000 

+  3,180 

-20.5 

+  29 

Ortho  bromcmnamic  acid.  .  . 

....  -  2,510 

+  3,280 

-19.5 

+  28  ' 

•B           m 

A. 

JB 

C 

Water  

0.46    137 

-21,420 

+29.9 

-0.085 

Orthoaminobenzoic  acid 

....0.60    179 

-17,770 

+23.2 

-0.084 

Pyridine  

....0.62    185 

-13,070 

+31.2 

-0.087 

2,  4,  6  Trimethyl  pyridine  .  . 

....0.84    250 

-11,980 

+48.2 

-0.060 

Ammonia  

....0.70    209 

-  8,625 

+32.6 

-0.085 

Acids  with  negative  heat  of 

diss.: 

Boric  acid  

..-1.67(-497) 

-  4,750 

-20.2 

-0.02 

p-Nitrophenol  

....0.21      63 

-  7,970 

+  4.5 

-0.035 

Ortho  aminobenzoic  acid  .  .  . 

0.68    203 

-  8,930 

+26.2 

-0.064 

220 


THEORIES   OF  SOLUTIONS. 


C2.  298  m 

Aminotetrazol 0.76  226 

Cinnamic  acid 0.39  116 

Benzole  acid 0.56  167 

Nitrourea  (at  20°) 0.94  277 

m-oxybenzoic  acid 0.30  89 

m-nitrobenzoic  acid 0.62  185 

Nitro-urethane 0.92  274 

Salicylic  acid 0.75  223 

Acids  with  positive  heat  of  diss.: 

Acetic  acid 0.30  89 

Ortho  toluylic  acid 0.27  80 

Ortho  chlorbenzoic  acid 0.41  122 

Ortho  iodbenzoic  acid 0.05  15 

Ortho  nitrobenzoic  acid 0.30  89 

Ortho  bromcinnamic  acid. .       .  .0.30  89 


12,800 

+42.2 

5,020 

+  12.0 

6,460 

+23.2 

18,350 

+93.5 

3,980 

+  7.7 

6,060 

+23.4 

1,258 

+59.7 

7,360 

+33.1 

5,360 

+14.6 

3,160 

+  7.8 

2,980 

+14.4 

770 

+  1.0 

340 

+  5.6 

890 

+  8.6 

•0.092 
-0.052 
-0.070 
-0.167 
-0.044 
-0.064 
-0.109 
•0.074 

•0.062 
-0.050 
-0.059 
-0.039 
•0.049 
•0.047 


These  figures  give  a  hint  to  many  rather  interesting 
conclusions,  which  will  be  more  obvious  if  we  smooth 
away  the  extremes  by  taking  average  values.  These 
are  for  the  three  groups: 


Water. 


n  A  V  A-U  dAldt 

1  -21,450  -13,450  -8,000  -27 

; .  4  -10.925  -  6,168  -4,157  -16 

Acids  with  neg.  U:.  10  -6,112  -2,121  -3,991  -13.4 

Acids  with  pos.  U:.   6  -4,183  +2,130  -6,313  -21 


2G  298 

Water 0.46 

Bases: 0.69 

Acids  with  neg.  U:  .0.61 
Acids  with  pos.  U:  .0.27 


Tm 

137 

206 

182.3 
81 


-21,420 
-12,861 

-  7,819 

-  2,250 


+29.9 

+33.8 
+32.3 
+  8.7 


dUldt 
+50 
+55 
+46 
+29.4 

C 

-0.085 
-0.080 
-0.077 
-0.051 


I  have  excluded  the  boric  acid,  which  behaves  quite 
differently  from  other  acids,  in  taking  the  mean  values. 
All  the  bases  possess  a  negative  value  of  U]  they  may 
therefore  be  compared  with  the  corresponding  acids. 
Although  the  heat  of  dissociation  is  about  three  times 
as  great  for  the  bases  as  for  the  corresponding  acids, 


THE   DOCTRINE   OF   ENERGY.  221 

the  value  A-U  is  of  nearly  the  same  magnitude  for  the 
two  groups.  The  values  dA  :  dt  and  dU  :  dt  are  also  not 
very  far  from  each  other  in  the  two  groups;  therefore 
the  same  holds  true  for  the  two  values  of  J5/2C.298 
and  Tm  (the  difference  here  reaches  12  per  cent.).  For 
the  acids  with  negative  U  (at  25°)  the  value  A  —  U  is 
55  per  cent,  greater  than  in  the  foregoing  two  groups, 
dA/dt  is  about  1.5  times  greater  and  dU  :  dt  on  the 
other  hand  only  0.6  of  the  mean  value  of  the  two  fore- 
going groups.  A  consequence  of  these  last  two  circum- 
stances is  that  Tm  lies  about  113°  lower  for  the  last 
group  than  for  the  two  first  ones.  At  this  temperature 
A  and  U  coincide  and  diverge  at  higher  temperatures, 
therefore  it  seems  quite  natural  that  A-U  shall  be  less 
for  the  two  first  groups,  where  the  distance  from  Tm 
to  the  temperature  of  measurement  is  only  104  degrees, 
than  for  the  third  group  for  which  the  corresponding 
distance  is  217  degrees.  Evidently  this  circumstance 
as  well  as  the  low  value  of  A0  is  connected  with  the 
positive  sign  of  U  at  25°  C.  for  this  last  group.  At 
higher  temperatures  other  acids  will  come  over  to  the 
third  group,  thus  for  example  m-oxybenzoic  acid 
already  at  29°  and  benzoic  acid  at  30°.  The  numerical 
values  of  A0,  B  and  C  decrease  continuously  from  the 
first  to  the  third  group,  A0  in  the  greatest  proportion, 
C  in  the  least. 

The  most  pronounced  regularity  is  that  dA  :  dt  is 
negative  and  dU  :  dt  positive  for  all  substances  exam- 
ined, and  that  for  all  (except  boric  acid,  which  is  very 
difficult  to  determine  accurately  because  of  its  extreme 
weakness)  the  numerical  value  of  dU  :  dt  exceeds  that 
of  dA  :  dt.  A  consequence  of  these  regularities  is  that 


222  THEORIES  OF  SOLUTIONS. 

Tm  for  all  examined  electrolytes  has  a  positive  value 
below  298°  (the  temperature  of  observation  =  25°  C.). 
The  two  highest  values  for  nitro-urea  and  nitro-urethane 
fall  at  +  4°  and  +  1°  C.,  after  these  comes  trimethyl- 
pyridine  with  —  23°  C.,  then  there  is  a  long  distance 
of  24  and  27°  C.  respectively  to  the  next  two,  aminotet- 
razol  and  benzoic  acid.  It  must  therefore  be  regarded 
as  characteristic  for  the  weak  acids  and  bases,  including 
water,  that  they  possess  A-  and  ^/-curves  which  inter- 
sect two  tunes,  not  only  at  T  =  0,  but  also  at  a  higher 
temperature,  and  that  they  diverge  from  that  tempera- 
ture, so  that  dA  :  dt  is  negative,  dU  :  dt  positive  and 
numerically  greater  than  dA  :  dt. 

Water  has  its  place  just  in  the  middle  of  the  two 
groups.  A  great  part  of  the  figures  given  above  are 
deduced  from  determinations  made  by  Lund£n,  the 
acids  from  aminotetrazol  except  acetic  acid  are  deter- 
mined by  other  authors.  If  we  now  compare  the 
values  of  Tm  according  to  the  measurements  of  Noyes 
and  those  of  Lunden,  we  find  a  certain  difference;  for 
water  176-137,  for  acetic  acid  119-89,  for  NH3 192-209. 
These  differences  are  of  course  due  to  experimental 
errors,  I  am  inclined  to  lay  a  great  value  on  LundSn's 
determinations  of  ammonia,  but  for  the  other  sub- 
stances the  determinations  of  Noyes  seem  preferable. 
The  phosphoric  acid  belongs  to  the  second  group  of 
acids,  its  dissociation  into  ions  is  accompanied  by  an 
evolution  of  about  1,600  cal.  at  25°.  Its  Tm  lies  higher 
(at  134°)  than  that  of  those  acids  in  general  (81°). 
I  suppose  according  to  Noyes'  measurements  that  the 
values  of  Tm  deduced  from  the  figures  given  by  Lunden 
are  a  little  too  low,  but  on  the  whole  this  difference  is 
of  minor  importance. 


THE  DOCTRINE  OF  ENERGY.  223 

We  have  seen  before  that: 

and    U  =  -  RT*d 

These  equations  are  sufficient  for  the  determination  of 
A  at  any  temperature  if  we  know  U  at  all  temperatures. 
For  then  we  know  A0  and  d  log*  K  :  dt,  i.  e.y  the  varia- 
tion of  A  with  temperature.  The  old  problem  of  the 
thermochemists,  to  determine  the  affinity,  is  therefore 
theoretically  solved  by  means  of  these  equations,  given 
by  van't  Hoff. 

But  practically,  there  are  rather  great  difficulties, 
which  depend  upon  our  lack  of  knowledge  of  the  values 
of  U,  the  heats  accompanying  chemical  processes  at 
all  temperatures  and  especially  very  low  or  very  high 
ones.  A  certain  theoretical  interest  is  attached  to  the 
vicinity  of  absolute  zero.  Of  course  aqueous  solutions 
do  not  exist  in  the  neighborhood  of  this  temperature, 
so  that  the  consequences  of  our  equations  cannot  be 
verified  there. 

There  A  is  negative  and  therefore  T  log,  K  is  negative 
and  has  a  definite  value;  f or  T  =  0  log,  K  becomes 
negative  and  infinite,  i.  e.,  K  =  0.  The  dissociation 
disappears  totally  at  absolute  zero.  Ions  cannot  exist 
at  absolute  zero,  just  as  the  vapors  of  liquids  on  simi- 
lar grounds  do  not  exist  in  the  neighborhood  of  abso- 
lute zero. 

It  is  of  a  certain  interest  to  remark  that  the  regu- 
larities are  much  more  prominent  with  the  process  of 
evaporation  than  with  that  of  solution  or  of  ionization. 
In  the  first  case  we  have  the  important  rule  of  Duhring, 
and  its  modification  by  Ramsay  and  Young,  as  well 


224  THEORIES  OF  SOLUTIONS. 

as  its  consequence,  the  rule  of  Trouton.  It  would  be 
rather  difficult  to  find  something  similar  for  the  solu- 
bility or  the  dissociation  of  electrolytes.  Regarding 
the  free  energy  on  evaporation  I  have  found  that 
the  coefficient  B  is  nearly  a  constant,  about  44  for  all 
substances.  The  curves  representing  A  therefore  run 
very  nearly  parallel  to  each  other.  As  we  have  seen 
above  for  the  three  groups  of  electrolytes  there  is  a 
certain  parallelism  between  the  magnitude  of  the 
constants  A0,  B  and  C,  so  that  they  are  greater  for 
the  bases  and  least  for  the  acids  with  positive  heat  of 
dissociation.  But  it  would  give  very  absurd  results 
if  one  supposed  that  this  rule  were  applicable  for  the 
comparison  of  two  electrolytes  chosen  at  random.  On 
evaporation  the  regularity  is  much  more  obvious  al- 
though not  complete. 

On  the  other  hand  the  multiplicity  and  variation  of 
the  phenomena  is  much  greater  in  electrolytic  dissocia- 
tion and  they  therefore  have  a  greater  attraction  for  the 
student  who  wishes  to  learn  all  possible  combinations 
appearing  in  the  central  problem  of  physical  chemistry, 
namely  that  regarding  chemical  equilibria.  This  prob- 
lem is  classical  here  in  the  world-renowned  Yale 
University,  where  one  of  the  greatest  thinkers  in 
natural  philosophy,  the  immortal  Willard  Gibbs,  has 
devoted  his  genius  to  the  investigation  of  chemical 
equilibria. 

At  the  close  of  my  lectures  I  feel  deeply  that  I  need 
to  tell  you  how  thankful  I  am  for  the  great  kindness  you 
have  always  shown  me  and  for  the  permanent  interest 
with  which  you  have  taken  part  in  my  lectures.  I  hope 
that  you  will  have  found  how  considerably  American 


THE  DOCTRINE  OF  ENERGY.  225 

scientists  have  contributed  to  the  most  modern  progress 
of  physical  chemistry.  I  am  quite  convinced  that  the 
development  will  go  on  still  further  hi  that  direction, 
and  I  am  glad  to  say  that  we  expect  very  much  from 
the  excellent  work  of  American  colleagues  with  their 
open  mind,  their  unrivalled  experimental  skill  and 
their  practical  sense. 


16 


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(1874-1878).    German  translation  by  Ostwald:  Thermodynamische 

Studien  (1892). 
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41,  11  (1902). 
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Verlagsges.  m.  b.  H.,  1910. 
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1885  and  1887,  2d  ed.,  1891,  1893,  1896-1902,  1906  (not  finished). 
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LECTURE   I. 

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M.  Berthelot  and  F.  Struntz:  Die  Chemie  im  Altertum  und  Mittelalter, 
Leipzig  and  Vienna,  Deuticke,  1909. 

P.Walden:Die  Losungstheorien  in  ihrer  geschichtlichen  Aufeinander- 
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J.  H.  van't  Hoff:  Studien  zur  chemischen  Dynamik,  ed.  by  E.  Cohen, 
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G.  Tammann:  Wiedemanns  Annalen,  68,  16,  1897;  Zeitschrift  f.  physi- 
kalische Chemie,  27,  323, 1898. 

E.  Lowenstein:  Zeitschrift  fur  anorganische  Chemie,  63,  69,  1909. 

L.  Th.  Reicher:  Groth's  Zeitschrift  fur  Kristallographie,  S.  593,  1883. 

J.  H.  van't  Hoff-E.  Cohen:  Studien  zur  chem.  Dynamik,  p.  187,  1896. 

E.  Cohen  and  C.  v.  Eyk:  Zeitschrift  f.  physik.  Chemie,  SO,  601,  1899. 

E.  Cohen:  Ibidem,  33,  57,  1900;  50,  225,  1905. 

W.  Hittorf :  Wiedmann's  Annalen  d.  Physik  u.  Chemie,  4,  409, 1878. 
Cf.  S.  Arrhenius,  Bihang  t.  K.  Vetenskapsakademiens  Handlingar, 
T.  8,  No.  14,  p.  19,  1884.  Ostwald's  Klassiker,  No.  160,  1907. 

226 


BIBLIOGRAPHICAL  EEFERENCES.  227 

W.  Ostwald :  Die  wissenschaf tlichen  Grundlagen  der  analytischen 
Chemie,  Leipzig,  Engelmann,  1894,  3d  ed.,  1901. 

H.  Dixon:  Trans.  Roy.  Soc.,  175, 617, 1884.  Journ.  Chem.  Soc.  Lond., 
49,  94  and  384,  1886. 

H.  B.  Baker:  Journ.  Chem.  Soc.  Lond.,  61,  728,  1892;  65,  611,  1894. 

D.  K.  Zavrieff:  Journ.  Soc.  phys.-chim.  russ.,  4%,  36,  1910. 

F.  Beilstein:  Handbuch  der  organischen  Chemie,  3d  ed.,  2,  79,  1896. 
H.  Goldschmidt:  Zeitschr.  f.  physikalische  Chemie,  60,  728,   1907. 

Zeitschr.  f.  Elektrochemie,  14,  581,  1908;    15,  10,    1909.     Cfr. 

Arrhenius:  Theorien  der  Chemie,  2d  ed.,  p.  202,  Leipzig,  Akad. 

Verlagsges.,  1909. 

LECTURE  II. 
B.  Richter:  Anfangsgrunde  der  Stochyometrie  oder  Messkunst  chy- 

mischer  Elemente,  Breslau,  1792-94. 

H.  Le  Chatelier:  Lemons  BUT  le  carbone,  p.  399,  Paris,  Hermann,  1908. 
H.  Roscoe  and  Harden:  Die  Entstehung  der  Dalton'schen  Atomhy- 

pothese  (Kahlbaums  Monographien,  H.  2),  Leipzig,  1890.      Cfr. 

W.  Ostwald:  Zeitschrift  fur  physikalische  Chemie,  69,  506,  1909. 
F.  Wald:  Zeitschrift  fur  physikalische  Chemie,  18,  337,  1895;  19,  607, 

1896. 
W.  Ostwald:  Faraday-lecture,   1904.    Journ.  Chem.  Soc.  Lond.,  25, 

518,    1904.    Principien   der   Chemie,    p.    383,    1907.    Leitlinien 

der  Chemie,  pp.  58,  64, 148, 153-155, 1906.    Leipzig,  Akademische 

Verlagsgesellschaft. 
L.  G.  Gouy:  Journal  de  physique  (2),  7,  561,  1888.    Older  literature  in 

O.  Lehmann:  Molekularphysik,  1,  264,  1888. 
The  Svedberg:  Nova  Acta  Reg.  Soc.  Scient.  Upsaliensis,  4,  2,  No.  1, 

1907;  ref.  by  Ostwald:  Zeitschr.  f.  phys.  Ch.,  64,  508,  1908. 
F.  Ehrenhaft:  Sitzungsberichte  d.  Wien.  Akad.,  Abt.  2a,  116, 1139, 1907; 

118,  321,  1909. 
Jean  Perrin:  Annales  de  chimie  et  de  physique,  (8)  18,  5-114,  1909. 

Journal  de  chimie  physique,  8,  57,  1910. 

E.  Rutherford  and  H.  Geiger:  Proceedings  of  the  Roy.  Soc.,  Ser.  A, 

Vol.  81,  162,  1908.     Jahrbuch  der  Radioaktivitat,  5,  415  (1908). 
J.  Dewar:  Proceedings  of  the  Royal  Society,  Ser  A,  Vol.  81,  280,  1908. 
B.  B.  Boltwood:  American  Journal  of  Science,  (4)  25,  493,  1908. 
J.  S.  Townsend:  Philosophical  Magazine,  (5)  45,  125,  1898. 

F.  Ehrenhaft:  Physikalische  Zeitschrift,  10,  308,  1909.    Sitzungsber. 

d.  Wiener  Akad.,  Abt.  II,  a,  119,  815,  1910. 
K.  Przibram:  Sitzungsberichte  d.  Wiener  Akad.,  Abt.  II,  a,  119,  1  and 

869,  1910.    Physikalische  Zeitschrift,  11,  630,  1910. 
M.  de  Broglie:  Comptes  rendus,  149, 1299,  1909.    Le  Radium,  7,  203, 

1909.     Physikalische  Zeitschrift,  11,  33,  1909. 


228  THEORIES  OP  SOLUTIONS. 

J.  Stark:  Physikalische  Zeitschrift,  5,  913,  1907;  9,  767,  1908.    J.  Stark 

and  W.  Steubing,  Physikalische  Zeitschrift,  9,  767,  1908. 
R.  Ladenburg:  Jahrbuch  f.  Radioaktivitat,  6,  425, 1910. 
J.  J.  Thomson:  Philosophical  Magazine,  (6)  20,  238,  1910. 
The  Svedberg:  Zeitschrift  f.  physikalische  Chemie,  74,  738,  1910. 
E.  Regener:  Ber.  d.  deutschen  phys.  Ges.,  6,  78,  1908.    Sitzungsber.  d. 

Berliner  Akad.,  1909,  p.  948. 
E.  v.  Schweidler:  First  international  Congress  for  radiology  and  ioniza- 

tion,  Liege,  1905,  Beiblatter,  81,  356,  1907. 
M.  v.  Smoluchowski,  Boltzmannfestschrift,  p.  626,  Leipzig,  1904. 
A.  N.  Meldrum:  Avogadro  and  Dalton,  Edinburgh,  James  Thin,  1906, 

pp.  63  and  65. 

LECTURE  III. 

H.  Schulze:  Journal  far  praktische  Chemie,  25, 431  (1882) ;  27, 320  (1883). 
Th.  Graham:  Philos.  Trans.  Lond.,  151,  183,  1861.     Liebig's  Ann.  d. 

Chemie  und  Pharmacie,  121,  1,  1862. 
G.  Bredig:  Zeitschrift  fur  angewandte  Chemie,  1898,  p.  951.    Zeitschrift 

f.  Elektrochemie,  4,  514  and  547,  1898. 
The  Svedberg:  Nova  Acta  Reg.  Soc.  Scientiarum  Upsaliensis,  4,  2, 

No.  1,  1907. 

The  Svedberg:  Arkiv  f.  Kemi,  T.  2,  No.  14  and  21,  1906;  No.  40,  1907. 
H.  Siedentopf  and  R.  Zsigmondy:  Drudes  Annalen  der  Physik,  10, 

1,  1903. 

A.  Cotton  and  Mouton:  Comptes  Rendus,  Paris,  136,  1657,  1903. 
R.  Zsigmondy:  Zeitschrift  f.  physikal.  Chemie,  56,  65  and  77,  1906. 

Cfr.    H.  Freundlich:    Kapillarchemie,  Leipzig,    Akad.    Verlags- 

gesellsch.,  1909,  p.  319. 
The  Svedberg :  Archiv  f .  Kemi,  Stockholm,  3,  No.  22, 1909.    Zeitschrift 

f.  physikalische  Chemie,  67,  105,  1909. 
A.  Coehn:  Ann.  d.  Physik,  (3)  64,  217, 1899. 
A.  Coehn  and  U.  Raydt :  Getting.  Nachr.,  1909,  p.  263.  Ann.  d.  Physik, 

(4)  80,  777,  1909. 

E.  F.  Burton:  Philosophical  Magazine,  (6)  11,  440,  1906. 
C.  Barus:  American  Journal  of  Science  (Silliman),  87,  122,  1889. 
G.  Bodlander:  Gottinger  Nachrichten,  1893,  p.  267. 
H.  Bechhold:  Zeitschrift  fur  physikalische  Chemie,  48,  385,  1904. 
W.  R.  Whitney  and  Al.  Straw:  Journal  of  the  American  Chem.  Society, 

29,  325,  1907. 
H.  Freundlich:  Zeitschrift  f.  physikalische  Chemie,  U>  129,   1903. 

Kapillarchemie,  p.  349. 
E.  Linder  and  H.  E.  Picton:  Journal  of  the  Chem.  Society  London,  87, 

1906, 1905. 
H.  Schulze:  Journal  fur  praktische  Chemie,  25, 431, 1882;  27, 320, 1883. 


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J.  Jacobson:  Zeitschrift  f.  physiologische  Chemie,  16,  349,  1891. 

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LECTURE  IV. 
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LECTURE  V. 

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170,  192  (1873).    Verh.  d.  naturhist.-med.  Vereins  zu  Heidelberg, 

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J.  H.  Van't  Hoff. 
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230  THEORIES  OF  SOLUTIONS. 

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(1879)  (German).    Ostwald's  Klassiker,  No.  104,  ed.  by  R.  Abegg. 

1899. 
W.  Tilden  and  W.  Shenstone:  Phil.  Trans.,  I.  (1884),  p.  30.  Rep.  Brit. 

Ass.,  1886,  449;  cited  by  P.  Walden  in  "Die  Losungstheorien,"  p. 

144,  1910. 
Dmitri  Mendelejeff:  Journ.  Russ.  phys.  chem.  Soc.,  16,  93,   184  and 

643  (1884);  cited  by  P.  Walden  in  "Die  Losungstheorien,"  p.  113, 

1910. 
G.^Kirchhoff:  Poggendorffs  Annalen  d.  Physik  und  Chemie,  103,  177 

(1858). 
C.  M.   Guldberg:    Christiania  Videnskabs  Selskabs  Forhandl.,  1867, 

pp.  140  and  156;   1868,  p.  15,  1870,  p.  1,  1872,  p.  136.    Ostwald's 

Klassiker,  No.  139,  ed.  by  R.  Abegg  (1903). 
J.  Willard  Gibbs:   Equilibrium  of  heterogeneous  substances.     Trans. 

Conn.  Acad.,  3,  108  and  343  (1874-1879).     German  ed.  by  W. 

Ostwald,  Leipzig,  1892. 
H.  v.  Helmholtz:  Sitzungsberichte  d.  Berliner  Akademie  der  Wissen- 

schaften,  1882,  p.  22. 
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(1885). 
J.  H.  van't  Hoff:   Archives  ne"erlandaises  (Haarlem),  20,  239  (1885). 

Recueil  des  travaux  chim.  des  Pays-Bas,  4,  424,  1885.    Svenska 

Vetensk.-Akad:s  Handlingar,  B.  21,  No.  17  (1885).     Zeitschr.  f. 

physikal.  Ch.,  1,  481,  1887.    Ostwald's  Klassiker,  No.  110,  ed.  by 

G.  Bredig,  1900. 
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(1884). 

M.  Traube:  Archiv.  f.  Anatomie  und  Physiologic,  1867,  p.  87. 
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physikalische  Chemie,  2,  415,  1888. 
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26,   1883.     Proces  verbaal  d.  Akad.  van  Wetensch.  Amsterdam 

1883. 
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1887.     Zeitschrift  f.  physikalische  Chemie,  1,  577,  1887. 

LECTURE  VI. 
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pp.  382,  387  and  389). 
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C.  A.  Valson:  Comptes  rendus,  Paris,  78,  441  (1871). 
P.  A.  Favre  and  C.  A.  Valson:  Comptes  rendus,  75,  330,  385,  798,  925, 

1000  and  1066  (1872). 

F.  Kohlrausch:  Wiedemann's  Annalen,  6,  168,  1879. 

H.  Gladstone:  Philosophical  Magazine,  (4),  36,  313  (1868). 
C.  Bender:  Wiedemann's  Annalen,  39,  89  (1890). 
H.  Jahn:  Wiedemann's  Annalen,  43,  280  (1891). 

G.  Wiedemann:  Poggendorff's  Annalen,  126,  1,  (1865);  135, 177(1868). 
A.  C.  Oudemans:  Liebig's  Annalen,  197,  48  and  66  (1879);  209, 38  (1881). 
H.  Landolt:  Ber.  d.  deutschen  chemischen  Gesellschaft,  6,  1073  (1873). 
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S.  Arrhenius:  Zeitschrift  fur  physikalische  Chemie,  8,  419  (1891). 
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6,  804,  1882,  and  Fortschritte  der  Physik  im  Jahre  1882,  part  2, 

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307  (1885). 

S.  Arrhenius:  Zeitschrift  fur  physikalische  Chemie,  4,  242  (1889). 
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232  THEORIES  OF  SOLUTIONS. 

LECTURE  VII. 
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Klassiker,  No.  29,  Leipzig,  1891. 
V.  Henri:  Zeitschrift  fur  physikalische  Chemie,  39,  194  (1901). 

C.  S.  Hudson:  Journal  of  the  American  Chemical  Society,  SO,  1160  and 

1546  (1908);  31,  655  (1909). 

A.  E.  Taylor:  Journal  of  biological  chemistry,  5,  405  (1909). 
E.  Duclaux:  Annales  de  1'Institut  agronomique,  10  (1886).    Ann.  Inst. 

Pasteur,  7,  751  (1893);  10,  168  (1896). 
E.  Buchner  and  J.  Meisenheimer:  Berichte  d.  deutschen  chem.  Ges., 

38,  620  (1905). 
M.  Nencki  and  N.  Sieber:  Journal  fur  praktische  Chemie,  (2)  24,  502 

(1881). 
A.  A.  M.  Hanriot:  Bulletin  dela  Socie*te*  chimique,  43,  417  (1885);  45, 

811  (1886). 

D.  Berthelot  and  H.  Gaudechon:  Compt.  rend.,  150,  1690  (1910). 

T.  Stoklasa  and  W.  Zdobnicky:   Biochem.  Ztschr.,  30,  433   (1911), 

Monatshefte  32,  53  (1911). 
Th.  Madsen:  Ofversigt  raf.  K.  Vetenskaps-Akademiens  Forhandlingar, 

1900,  No.  6,  p.  818."    Zeitschr.  f.  phys.  Ch.,  86,  290  (1901). 
J.  J.  A.  Wijs:  Zeitschrift  f.  physikalische  Chemie,  11,  521  (1893);  12, 

514  (1893). 
Thor  Carlson:  Meddelanden  fran  K.    Vetenskapsakademiens  Nobel 

institut,  2 ,  No.  9,  1911. 
S.  Arrhenius:  Meddelanden  fran   K.  Vetenskapsakademiens  Nobel- 

institut,  1,  No.  9  (1908). 

E.  Schfitz:  Zeitschrift  f.  physiologische  Chemie,  9,  577  (1885). 

T.  Sjoqvist:  Skandinavisches  Archiv  f.  Physiologic,  5,  317  (1895). 

W.  Stade:  Hofmeister's  Beitrage,  S,  291  (1902). 

S.  Arrhenius:  Immunochemistry,  New  York,  Macmillan  Co.  (1907), 

pp.  65-87  and  119-127. 

R.  Kremann:  Wiener  Sitzungsberichte,  119,  83,  141  and  483  (1910). 
E.  Rutherford:  Radioactivity,  2  ed.,  Cambridge,  1905,  pp.  325,  366  and 

376. 

J.  H.  vant  Hoff:  Etudes  de  dynamique  chimique,  Amsterdam,  1884. 
M.  Berthelot:  Annales  de  chimie  et  de  physique,  (3)  66, 110  (1862). 
S.  Arrhenius:  Zeitschrift  fur  physikalische  chemie,  4,  226  (1889). 
J.  H.  van't  Hoff:  Etudes  de  dynamique  chimique,  Amsterdam,  1884. 

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D.  M.  Kooy:  Zeitschrift  fur  physikalische  Chemie,  12,  155  (1893). 
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LECTURE  VIII. 

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C.  M.  Guldberg  and  P.  Waage:  Journal  f.  praktische  Chemie,  127,  82 

(1879).    Ostwald's  Klassiker,  No.  104,  S.  138  (1899). 
T.  Cundall:  Journ.  of  the  Chemical  Society,  59, 1076  (1891).    Cf.  van't 

Hoff's  Vorlesungen,  2d  ed.,  I,  110  (1901). 
W.  Ostwald:  Zeitschrift  f.  physikalische  Chemie,  8,  170,  241  an<T369: 

(1889). 

G.  Bredig:  Zeitschrift  f.  physikalische  Chemie,  13,  289  (1894). 
J.  H.  van't  Hoff:  Zeitschrift  f.  physikalische  Chemie,  18,  300  (1895). 
F.   Kohlrausch:   Zeitschrift   f.   Elektrochemie,   14,   132    (1908).    Cf. 

E.  Rasch  and  W.  Hinrichsen,  ibid.,  p.  46. 

A.  A.  Noyes,  A.  C.  Melcher,  H.  C.  Cooper  and  G.  W.  Eastman:  Car- 
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W.  Ostwald:  Zeitschrift  fur  physikalische  Chemie,  1,  74  and  97  (1887). 

Cf.  P.  Walden:  ibidem,  1,  529  (1887),  2,  79  (1888);  8,  775  (1891). 
A.  A.  Noyes:  Congress  of  arts   and   science  S.  Louis,  1904,  4,  317. 

Technology  quarterly,  17,  300  (1904).    Science,  20,  582  (1904). 
S.  Arrhenius:  Zeitschrift  fiir  physikalische  Chemie,  2,  296  (1888). 


:234  THEOKIES   OF   SOLUTIONS. 

T.  Godlewski:  BuUetin    of   the  Academy  of    Cracow,  6,  239,  1904. 

Zeitschr.  f.  physik.  Ch.,  51,  751  (1905). 
E.  Hagglund:  Arkiv  f.  Kemi,  Stockholm,  4,  No.  11,  1911. 
G.  Wiedemann:  Poggendorff's  Annalen,  99,  229  (1856).     Die  Lehre 

v.  d.  Elektricitat,  2,  947  (1883). 
C.  Stephan:  Wiedemann's  Annalen,  17,  673  (1882). 
E.  Bouty:  Journal  de  physique,  (2)  3,  351  (1884). 
Fr.  Kohlrausch:  Proc.  Roy.  Soc.,  71,  338  (1903).     Cf.  Zeitschrift  fur 

Elektrochemie,  14,  130  (1908). 

S.  Arrhenius:  Zeitschrift  f.  physikalische  Chemie,  9,  497  (1892). 
P.  Walden:  Zeitschrift  fur  physikalische  Chemie,  55,  207  (1906). 
P.  Dutoit  and  H.  Rappeport :  Journal  de  chimie  physique,  6,  545  (1908). 
P.  Dutoit  and  H.  Duperthuis:  Journal  de  chimie  physique,  6,  726  (1908). 
M.  R.  Schmidt  and  Harry  Jones:  American  chem.  journal,  42,  37  (1909). 
P.  Walden:  Zeitschrift  f.  physikalische  chemie,  73,  257  (1910). 
J.  Kunz:  Zeitschrift  f.  physikalische  Chemie,  42,  591  (1903),  Inaugural 

dissertation,  Zurich,  1902. 

W.  H.  Green:  Joura.  Chem.  Soc.  Lond.,  98,  2023  and  2049  (1908). 
L.  Pissarshewski  and  A.  Schapowalenko:  Journ.  Russ.  Phys.-Chem. 

Soc.,  42,  905,  1910.     Chem.  Zentralbl.,  81,  1849  (1910). 
T.  Johnston:  Journal  American  Chem.  Soc.,  31,  1010  (1909). 
H.  M.  Goodwin  and  R.  D.  Mailey:  Trans.  Amer.  Electroch.  Soc.,  11 , 

211  (1907),  Journ.  Chem.  Soc.  Lond.,  92,  931  (1907). 
H.  M.  Goodwin  and  H.  T.  Kalmus:  Physical  Review,  27,  322  (1908). 
K.  Arndt  and  A.  Gessler:  Zeitschrift  f.  Elektrochemie,  1 4,  662  and  665 

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B.  D.  Steele,  D.  Mclntosh  and  E.  H.  Archibald:  Trans.  Roy.  Soc.  Lond., 

A,  205,  99  (1905). 
H.  W.  Foote  and  N.  A.  Martin:  Journ.  American  Chem.  Society,  41  >  451 

(1907).    Chemisches  Centralblatt,  80,  II,  887  (1909). 
J.  W.  Walker  and  F.  G.  Johnson:  Journ.  Chem.  Soc.  Lond.,  87,  1597 

(1905). 
P.  Walden  and  M.  Centnerszwer:  Zeitschrift  f.  physikalische  Chemie, 

39,  525  (1902). 

Edward  C.  Franklin:  Zeitschrift  f.  physikalische  Chemie,  69,  272  (1909). 
W.  Hittorf:  Poggendorff's  Annalen,  106,  547  (1859). 
A.  Ssacharow:  Journ.  Russ.  Phys.  Chem.  Soc.,  42,  683  (1910).    Chemi- 
sches Zentralblatt,  81,  1523  (1910). 
L.  Kahlenberg  and  O.  Ruhoff:  Journal  of  Physical  Chemistry,  7,  254 

(1903). 

R.  Lorenz:  Zeitschrift  f.  physikalische  Chemie,  70,  230  (1910). 
G.  Carrara:  Mem.  della  R.  Ac.  dei  Lincei,  (5)  6,  268  (1906). 
P.  Walden:  Zeitschrift  fur  physikalische  Chemie,  73,  257  (1910). 


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236  THEORIES   OF   SOLUTIONS. 

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J.  Shields:  Zeitschrift  fur  physikalische  Chemie,  12,  167  (1893). 

J.  Walker:   Zeitschrift  fiir  physikalische  Chemie,  4,  319  (1889).    Cf« 

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A.  Hantzsch:  Berichte  d.  deutschen  chem.  Ges.,  35,  210  (1902). 
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H.  Lunde"n:  Journal  de  chimie  physique,  5,  145  (1907). 
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L.  Kahlenberg:  Trans.  Wisconsin  Academy,  15,  209  (1906).     Journ.  of 

Physical  Chemistry,  10,  141  (1906) 

E.  Cohen  and  J.  W.  Commelin:  Zeitschrift  fur  physikalische  Chemie, 

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LECTURE  X. 

J.  H.  van't  Hoff:  Zeitschrift  f.  physikalische  Chemie,  18,  300  (1895). 
H.  Jahn:  Zeitschrift  f  physikalische  Chemie,  S3, 545  (1900) ;  35, 1  (1900). 
S.  Arrhenius:  Zeitschrift  f.  physikalische  Chemie,  36,  28  (1901);  37, 

315  (1901). 

R.  Abegg:  Zeitschrift  f.  Elektrochemie,  13,  18  (1907). 
K.  Drucker :  Die  Anomalie  der  starken  Elektrolyte.   Ahren's  Sammlung 

chem.  u.  chem.  -techn.  Vortrage,  1905,  No.  1  and  2. 
H.  von  Steinwehr:  Zeitschrift  f.  Elektrochemie,  7,  685  (1901). 
C.  Liebenow:  Zeitschrift  f.  Elektrochemie,  8,  933  (1902). 
R.  Malmstrom:  Annalen  der  Physik,  (4)  18,  413  (1905). 

F.  A.  Kjellin:  Arkiv  for  Kemi,  4,  No.  7,  Stockholm,  1910  (Swedish). 
Ch.  Blagden,  F.  Rudorff  and  L.  De  Coppet:  See  Ostwalds  Lehrb.  d.  allg. 

Ch.,  1  ed.,  T.  1,  pp.  407-465  (1885);  2  ed.,  T.  1,  p,  742-748  (1891). 
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Washington,  Publ.  No.  60  (1907),  Am.  Chem.  Journ.  38,  683  (1907). 

39,  313  (1908). 

R.  Abegg:  Zeitschrift  f.  physikal.  Chemie,  15,  209  (1894). 
H.  N.  Morse  and  coworkers:  Amer.  Chem.  Joum.,20, 80;  28, 1;  34, 1;  36, 

1;  37,  324,  426  and  558;  38,  175;  39,  667;  40,  1,  194,  266  and  325; 

41, 1  (1901-1909). 
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Phil.  Trans.,  A,  206,  481  (1906). 

0.  Sackur:  Zeitschrift  f.  physikalische  Chemie,  70,  477  (1909). 
A.  A.  Noyes:  Zeitschr.  f.  phys.  Chemie,  5,  83  (1890).    Cfr.  G.  Bredig; 

ibidem,  4,  444  (1889). 
E.  W.  Washburn:   Jahrbuch  f.  Radioaktivitat,  5,  493  (1908);   6,  69 

(1909). 


BIBLIOGRAPHICAL  EEFERENCES.  237 

G.  Tammann:  Zeitschrift  fur  physikalische  Chemie,  9,  97  (1892). 
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S.  Arrhenius:  Zeitschrift  L  physikalische  Chemie,  1,  110  (1887),  and 

4,  226  (1889). 

S.  Arrhenius:  Zeitschrift  f.  physikalische  Chemie,  SI,  197  (1899). 
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H.  C.  Jones:  Zeitschrift  fur  physikalische  Chemie,  13,  419  (1894). 
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G.  Tammann:  Zeitschrift  f.  physikalische  Chemie,  16,  139  (1895). 
W.  Ostwald:  Journal  fur  praktische  Chemie,  (2)  16,  385  (1877)  and  (2) 

18,  328  (1878). 

T.  Fanjung:  Zeitschrift  fur  physikalische  Chemie,  U,  673  (1894) 
P.  Drude  and  W.  Nernst:  Zeitschrift  fur  physikalische  Chemie,  15, 

79  (1894). 
G.  Carrara  and  M.  G.  Levi:  Gazz.  Chim.  italiana,  SO,  II,  197  (1900), 

Zeitschr.  f.  phys.  Chemie,  86,  105  (1901). 

P.  Walden:  Zeitschrift  fur  physikalische  Chemie,  60,  87  (1907). 
W.  R.  Bousfield:  Zeitschrift  f.  physik.  Chemie,  53,  257  (1905). 
W.  Ostwald:  Zeitschrift  f.  physikalische  Chemie,  2,  840  (1888). 
G.  Bredig:  Zeitschrift  fur  physikalische  Chemie,  13,  191  (1894). 
W.  Nernst,  C.  C.  Garrard  and  E.  Oppermann:  Gottinger  Nachrichten, 

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R.  B.  Denison  and  B.  D.  Steele:  Zeitschrift  fur  physikalische  Chemie, 

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G.  Bredig:  Zeitschrift  fur  physikalische  Chemie,  13,  228-238  (1894). 

LECTURE  XI. 
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pp.  37  and  52-54  (1886). 

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238  THEORIES  OF  SOLUTIONS. 

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INDEX  OF  AUTHORS. 


ABEGG,  175,  176,  178 

Alexejew,  31 

Amagat,  69 

Anaximenes,  1 

Arago,  77 

Archibald,  148,  149 

Aristoteles,  2,  4,  5 

Arndt,  146 

Arrhenius,  52,  60,  87,  88, 101, 108- 

111, 124, 127, 130, 136, 156, 164, 

167,  180,  202,  218 
Aure"n,  126 
Avogadro,  20,  21,  34,  35 

BABO,  VON,  131 

Baker,  14 

Bartoli,  107,  108 

Barus,  43 

Baur,  xix 

Bechhold,  44 

Begeman,  30 

Bellati,  76 

Bender,  96 

Berkeley,  Earl  of,  176 

Berthelot,  D.,  116 

Berthelot,  M.,  87,  102,  109,  123, 

132,  153,  154,  204 
Berthollet,  9,  10,  11,  18,  75,  76 
Berzelius,  19,  103,  112 
Biltz,  50 
Bizio,  76 
Bjemim,  31 
Blagden,  174,  175 
Bodenstein,  128 
Bodlander,  43 
Boltwood,  25 
Boltzmann,  20,  79,  84,  89 
Bousfield,  185-187,  191,  193 
Bouty,  140 
Boyle,  4,  5,  86,  177 
Bredig,  37,  46,  49,  111,  133,  134, 

159,  187,  195, 
Broensted,  217 
Broglie,  de,  31 
Brown,  22 
Buchboeck,  118 
Buchner,  115 


Buetschli,  51 
Buffon,  7 
Bunsen,  131 
Burton,  43 

CAHOURS,  83 

Carlson,  117 

Carnot,  82 

Carrara,  152,  184 

Cauchy,  26 

Cavendish,  17 

Centnerszwer,  149 

Chappuis,  65 

Clapeyron,  82,  131 

Clausius,  20,  79,  91,  106-108 

Coehn,  40,  189 

Cohen,  13,  170 

Commelin,  170 

Coppet,  de,  174 

Cotton,  38 

Coulomb,  112 

Cundall,  132 

DALTON,  18-20,  34,  35 

Dawson,  155 

Debray,  82 

Democritus,  5 

Denison,  190,  191 

De  Vries,  85,  86-88,  98 

Dewar,  25 

Ditte,  87 

Dixon,  14 

Drude,  184 

Du  Bois  Reymond,  56 

Duclaux,  115 

Diihring,  223 

Duperthiis,  144 

Dutoit,  143,  144 

EDGAR,  165 

Ehrenhaft,  22,  23,  27-33 

Einstein,  23,  24,  31,  40,  200 

Empedocles.  1 

Erfle,  26 

Euler,  129 

FAMULENER,  129 


239 


240 


INDEX  OF  AUTHORS. 


Fanjung,  183 
Faraday,  25,  27 
Favre,  94,  95 
Fink,  49 
Fontana,  55 
Foote,  148 
Franklin,  150,151 
Freundlich,  45,  48 

GARRARD,  188 

Gassendi,  5,  34 

Gay-Lussac,  20,  35,  74-77,  86,  91, 

103,  104,  106-108 
Geiger,  25,  30 
Gessler,  146 
Gibbs,  Willard,  xvii,  70,  83,  84,  87, 

224 

Gladstone,  96 

Godlewski,  137,  138,  169,  170 
Goldschmidt,  15,  208 
Goodwin,  145,  147 
Gore,  14 
Gouy,  22 
Graham,  37 
Green,  145 
Grotthuss,  105,  139 
Guldberg,    77-84,    87,    109,    127, 

131-133,  165-167 

HAGGLUND,  137 

Hannot,  115 

Hantzsch,  169 

Hartley,  176 

Helmholtz,  H.  v.,  27,  84,  87,  108, 

163 

Helmholtz,  R.  v.,  30 
Helmont,  van,  3, 17 
Henri,  113,  114 
Henry,  56,  87, 153 
Heraclitus,  1 
Hess,  96 

Heydweiller,  111,  180,  181 
Hittorf,  14,  134,  150,  188-192 
Homfray,  Miss,  63,  64,  67,  68 
Horstmann,  77,  78,  83 
Hudson,  113 

ISAAC  HOLLANDUS,  3 

JACOBSON,  48,  49 
Jahn,  96,  173,  195, 
Jellet,  87 
Johnson,  148 
Johnston,  141 


Jones,  144,  175,  180 
Jungfleisch,  87,  153,  154 

KAHLENBERG,  151,  170 

Kalmus,  147 

Kirchhoff,  81,  131 

Kjellin,  174 

Klein,  10 

Klobbie,  205 

Kohlrausch,  96, 109,  111,  134, 140, 

145,  184-186 
Kooy,  124 
Koppel,  187 
Kossel,  161 
Kremann,  121,  125 
Kunckel,  4 
Kunz,  145 

LADENBURG,  32,  33 

Landolt,  96 

Landsteiner,  71 

Latley,  30,  31 

Lavoisier,  8,  9,  17 

Le  Chatelier,  4,  18,  22,  84,  87,  206 

Lemery,  5 

Lenz,  162 

Levi,  184 

Lewis,  70 

Ley,  169 

Lincoln,  169 

Linder,  45 

Loewenstein,  10 

Lorentz,  26,  30 

Lorenz,  151 

Loschmidt,  30 

Lowitz,  55 

Lunden,  159,  160, 169,  218,  222 

MADSEN,  116,  129 
Mailey,  145 
Malikow,  31 
Mallard,  10 
Malmstrom,  174 
Marignac,  82 
Martin,  145,  148 
Masson,  145 
Maxwell,  20,  79 
McCrae,  155 
Mclntosh,  148,  149 
Meisenheimer,  115 
Mendelejew,  80,  81 
Michaelis,  71 
Millikan,  28,  30,  31 
Moore,  155 


INDEX  OF  AUTHORS. 


241 


Moreau,  31 
Morse,  175 
Monton,  38 
Muller  v.  Berneck,  46 

NABL,  30 

Nencki,  115 

Nerast,    xx,    154,    162-164,  184, 

188,  216 

Newton,  6,  7,  74,  112 
Noyes,   xix,   134,   136,   140,   141, 

144,  176,  194,  208,  209,  213,  222 


,  52 
Oholm,  162 
Ohm,  106 
Olympiodoros,  3 
Oppermann,  188 
Ostwald,  xx,    14,   21,  22,  26,  87, 

109-111,     132-135,     158,    167, 

182,  183,  187,  199 
Oudemans,  96 

PARACELSUS,  4 

Partington,  180 

Payen,  55 

P6an  de  St.  Gilles,  132 

Pebal,  161 

Pellat,  30 

Perrin,  22-27,  31,  32,  36,  39 

Pfeffer,  85,  86 

Picton,  45 

Pissarshewski,  145 

Planck,  26,  30,  32,  33,  89,  111,  133, 

163 

Plato,  2,  5 
Pleijel,  163 
Plotnikow,  126,  127 
Pollitzer,  200 
Price,  125 
Proust,  9,  18 
Przibram,  28-32 

RAMSAY,  63,  223 

Raoult,  82,  87,  98-100,  110,  176 

Rappeport,  143 

Rappo,  51 

Rayleigh,  26 

Re'aumur,  6 

Regener,  25,  31,  33 

Regnauld,  22 

Reicher,  111 

Reinhold,  188,  191,  193 

Reuss,  40 


Richarz,  30 
Richter,  9,  17 
Riesenfeld,  188,  191,  193 
Rivett,  178 
Robertson,  161 
Rontgen,  96,  98 
Rona,  71 
Rosenstiehl,  77 
Rothmund,  205 
Roux,  31 

Rudorff,  82,  174,  175 
Runoff,  151 
Rutherford,  25,  30,  122 

SACKUR,  176 
Sainte-Claire-Deville,  93 
Sammet,  xix 
Saussure,  de,  55 
Schapowalenko,  145 
Sche"ele,  C.,  18 
Sch<§ele,  R.,  55 
Schimpff,  200 
Schmidt,  G.  C.,  57,  59-62 
Schmidt,  M.  R.,  144 
Schneider,  96,  98 
Schiitz,  119,  120 
Schulze,  45,  50 
Schweidler,  v.,  33 
Shenstone,  80 
Shields,  168 
Sieber,  115 
Siedentopf ,  38 
Sjoqvistll9 
Smits,  125 

Smoluchowski,  v.,  22,  23,  33 
Soleil,  112 
Spohr,  166 
Spring,  127 
Ssacharow,  151 
Stade,  119 
Stahl,  6 
Stark,  32 

Steele,  148, 149,  190,  191 
Stefan,  30,  70 
Steinwehr,  v.,  174 
Stokes,  23,  31,  185 
Stoklasa,  116 
Stoney,  30 
Straw,  44 

Svedberg,  22, 23, 34, 36, 38, 40, 46, 
50,  52,  177 

TABOR,  31 

Tammann,  10, 177, 178 


242 


INDEX  OF  AUTHORS. 


Taylor,  A.  E.,  114 

Thales,  1 

Thomsen,  Jul.,  79,  87,  102,  109, 

131,  204 

Thomson,  J.  J.,  30,  33 
Tilden,  80 

Titoff,  63-68 
Townsend,  30 
Traube,  M.,  85 
Travers,  57,  58 
Trouton,  224 
Tyndall,  38 

UGGLAS,  Miss  BETH  AF,  129 
Uhlirz,  71 

VALSON,  80,  91-95,  101-103,  108 

Van  der  Waals,  67,  69,  70,  176 

Van  Name,  165 

Van't  Hoff,  4,  81,  82,  84, 110,  111, 
122-126,  129-133, 136, 155, 170- 
174,  196,  199,  200,  204,  206- 
208,  223 

WAAGE,  77-79,  83,  107,  109,  127, 

132,  133,  165-167 
Wakeman,  169 
Wald,  21,  22 


Walden,  70, 142, 144, 149, 152, 184 

Walker,  T.  W.,  148 

Walker,  J.,  159,  160,  168 

Wallach,  49 

Washburn,  177,  179,  188-192,  194 

Whitney,  44 

Wiedemann,  G.,  96,  140 

Wiedemann,  E.,  101-103 

Wien,  W.,  30 

Wijs,  117 

Wilhelmy,  112,  113,  123 

Williamson,  91, 103,  104, 106, 107, 

120,  121 

Wilson,  H.  A.,  30,  31 
Winkelblech,  159,  160 
Witkowski,  108 
Wolff,  125 
Wollaston,  19 
Wullner,  82 
Wiirtz,  83 

XENOFANES,  1 
YOUNG,  223 

ZAVRIEFF,  14 
Zsigmondy,  38,  40,  51 


INDEX  OF  SUBJECTS. 


ABNORMAL  electrolytes,  147-151 
Absorption  of  light,  128 
Acetic  acid,  156,  210 
Aceton,  169 

Acids,  6,  17,  18,  42-44,  48,  53,  72, 
109,  112,  113 

weak,  157-158, 179, 182,  219- 

222 

Acid  salts,  166 
Active  molecules,  108 
Activity,  109 
Additive  properties,  91-103 

scheme,  92,  97 

Adsorption,  39,  43,  55-71, 122, 157 
Affinity,  9,  74,  75,  196-225 

tables  of,  7 
Aggregation,  70 

state  of,  2 
Agglutinins,  157 
Albuminous  substances,  161 
Alcahest,  4 
Alcohol,  115,  169 
Alcoholic  solutions,  137 
Allotropy,  11,  13,  21 
Alpha-particles,  25,  33 
Alums,  decomposition  in  solution, 

95 

Amido-acids,  158-161 
Amines,  150,  151 
Ammonia,  131,  150,  151,  156,  183, 

210 

Amphoteric  electrolytes,  158-161 
Analogy  between  gases  and  dis- 
solved matter,  72-90,  110,  131, 
132,  170,  171 
Analysis,  110,  111 
Anilin  acetate,  168 
Aqueous  atmosphere  of  ions,  185 
Arsenious  acid,  188 
Atoms,  5 
Atomic  volume,  185,  187 

weight,  18,  54 
Attraction,  1 

molecular,  67,  68,  70 
Autocatalysis,  116,  117 
Autoclaves,  113 
Avidity,  87,  167,  168 


Avogadro's  law,  20,  34,  35 

BACILLI,  117,  156 

Bases,  6,  42,  43,  72,  109,  219-222 

Benzene,  15,  156 

Beta-rays  27,  122 

Bimolecular  reactions,   122,   125, 

128 

Bivalent  ions,  135,  141 
Blood-corpuscles,  156 
Boric  acid,  146,  188,  202 
Brownian  movement,  22,  34,  39 

CALCIUM  hydrate,  203 

Caloric,  8 

Caoutchouc,  170 

Capillarity,  see  Surface  tension 

Capillary  height,  91-93,  98 

Carbonates,  19 

Carbonic  acid,  3,  115,  125,  148 

Carnot's  theorem,  82 

Casein,  161 

Catalytic  action,  48,  103,  110,  112 

Cathode  rays,  27 

Cells,  85,  156,  157 

Charcoal,  55-68 

Chemical  force,  77 

Chemical  processes,  10-14 

Chlorophyll,  116 

Coagulation,  119 

Coexistent  phases,  13,  51 

Cohesion,  75 

Colloidal  solutions,  32,  37,  71 

Color,  see  Optical  properties 

Coloring  matter,  55 

Complexity.  76,  100,  148-151,  191 

Compressibility,  68,  96 

Concentration,  77,  78,  80 

Concentration  cells,  162,  163 

Conductivity,  electric,  14, 96, 106- 

110,  195 

Constant  proportions,  9,  18,  71 
Contraction,  6,  10,  95,  182-184 
Corpuscular  theory,  5,  6 
Cosmogonical  ideas  on  solutions,  1 
Co-volume,  176 
Critical  temperature,  67,  70,  206, 

207,  214 


243 


244 


INDEX  OF  SUBJECTS. 


Crystal  form,  5 

water,  6,  10,  181,  187,  191 
Crystalloids,  37 

DECOLORATION,  55,  62 
Dehydration,  120 
Deliquescent  salts,  9 
Density,  80,  81,  91,  94,  98 

modules,  181 
Dibasic  acids,  158 
Dielectricity  constant,  184,  187 
Diffraction,  50 
Diffusion,  39,  40,  74, 108, 161-164, 

178,  185 

Digestion,  116,  119 
Disgregation,  78 
Dispersing  action,  53,  54 
Dissociation  constants,  159,  160, 

169,  170,  192 
Dissociation,  degree  of,  100,  101, 

108, 134, 135, 142, 147, 159, 

167, 179,  183 
theory,  12,  14,  16,  82,  83,  95, 

107,  147,  151,  152 
Dissolution,  7 
Droplets,  14,  23,  24,  26,  28 
Dualistic  electrochemical  theory, 

99 
Dyeing  processes,  55 

EGG-WHITE,  119,  129 
Electric  charge  of  suspended  par- 
ticles, 40-42 
endosmose,  42 
fields,  30,  31,  105 
forces,  163,  164,  172 
transport  (see  also  Migration), 

42,  189 

Electrolytic  dissociation,  76,  88, 
91-111,  133,  148,  164,  198,  199, 
209-223 
Electromotive  force,  87,  107,  108, 

162,  163 
Electrons,  27 
Electrostriction,  184,  187 
Elementary  electric  charge,  25-27, 

30,  31,  104 
Elements,  chemical,  19 

four,  1,  4,  19 
Emulsions,  24,  122 
Energy,  88,  196-225 

radiant,  32 

Enzymes  (see  also  Ferments),  113, 
114,  119,  129,  130 


Equilibrium,    change    with    tem- 
perature, 155 
chemical,  11,  72,  77,  78,  84, 

87,  109,  154,  166-170 
heterogeneous,  131,  197 
homogeneous,  132,  136,  148, 

153-171,  198-200 
Equipollency,  76,  103 
Equivalents,  34 
Esters,  formation  of,  15,  123 
Ethylene,  126 
Ethyl  ether,  103,  120,  121,  126, 

156,  205 

Evaporation,  196,  214,  215 
Exchange  of  radicals,  75,  104 

FARADAY'S  law,  25-27,  104,  162 

Fats,  119 

Ferments  (see  also  Enzymes),  48, 

120 

Fever,  129 
Fluidity   (see  also  Viscosity),  2, 

137-149,  194,  195 
Foreign  substances,  78,  165,  172, 

179 

Free  energy,  84,  87,  196-224 
Freezing  points,  98-100,  110,  177, 

178 

Fulminating  gas,  46 
Fused  electrolytes,  145-147,  151 

GAMMA-RAYS,  122 

Gas-laws,  177,  196 

Gas-reactions,  125,  132 

Gastric  juice,  119 

Gay-Lussac's  law,  20,  35,  197 

Gelatine,  51 

Gels,  119 

Glucose,  115,  116 

Gravitation,  6,  7 

Growth,  117 

Guldberg  and  Waage's  law,  77-79, 

83,  87,  109-111,  133,  167,  172, 

195,  198 

ILEMOLYSINS,  129 

Heat  effect,  10,  11,  199 
of  activation,  109 
of  adsorption,  65 
of  combination,  94,  101 
of  compression,  69 
of  dilution,  79,  131 
of  dissociation,  83,  84,  111, 
210-212,  218-228 


INDEX  OF   SUBJECTS. 


245 


Heat  effect  of  evaporation,  214-21 
of  hydration,  155 
of  neutralization,  102-109 
of  solution,  131,  155,  202-209 
of  substitution,  101,  102 
of  suspension,  52 
radiation  of,  26 

Helium,  25 

Henry's  law,  153 

Hydrated  ions,  140,  172,  184, 189- 
195 

Hydrates,  181,  187 

Hydration,  12.  175,  179,  180 

Hydriodic  acid,  128 

Hydrogen  ions,  45,  53,  114-117, 
125,  138-140,  181,  182 

Hydroxyl  ions,  44,  114-117,  125, 
138-140,  181,  182 

Hydrolysis,  37,  109,  112,  114,  168, 
169 

Hygroscopicity,  56 

ICE,  12 

molecules,  182 
Iceland  spar,  127 
Immune-bodies,  157 
Inactive  molecules,  108 
Increase  of  boiling  point,  81 
Infinite  dilution,  134 
Inner  salts,  159 
Inorganic  ferments,  48 
Integral  reactions,  21 
Intermediary  products,  120,  122 
Inversion  of  cane-sugar,  112-116, 

123,  125 

Invertase,  113,  129 
Ionic  conductivity,  134,  142,  193 
Ionic  friction,  162,  172,  173 
Ion-product,  160 
Ions,  radii  of,  185 
Isohydric  solutions,  136 
Isonitrosoketones,  169 
Isotherm,  58 
Isotonic  coefficient,  88,  110,  207, 

208 
Isotonic  solutions,  85,  87 

JELLY,  51 

KINETIC  theory  of  heat,  20,  79, 
94,  106 

LACTIC  acid,  115 
Lsevulose,  115,  116 


Lead,  2,  5 

Lecture  experiments,  xviii,  xix 

Life-elixir,  4 

Light,  diffusion,  refraction,  wave- 
length, 26 

Lipases,  119 

Lowering  of  freezing  point,  81,  87, 
98-100,  149,  153,  174 

MAGNETIC  rotation,  96 
Magnetism,  molecular,  96 
Maltase,  maltose,  114 
Mannite,  188 
Mass-action,    see    Guldberg    and 

Waage's  law 

Maximum   effect,   47,  48,  53,  54 
Mercury,  2 
Mercuric  sulphate,  9 
Metals,  2,  6 

solution  of,  126,  127 
Migration  of  ions,  148,  190-193 
Mixtures,  osmotic  pressure  of,  177, 

178 

Moisture,  14 
Molecular   conductivity,  147-155 

heat,  200 

weight,  156 
Molecules,  5,   11,  153 
Monomolecular  reactions,  46-48, 

122,  125,  128 

Monovalent,  ions  42-45,  135,  141 
Movement  of  ions,  95, 105, 185 
Multiple  proportions,  18,  19 
Mutarotation,  114 

NAPHTHALENE,  156 
Neutralization,   17-19,   102,   181, 

182 

Nitration,  15 
Nitric  acid,  15 
Nitro-compounds,  169 
Nitrogen  peroxide,  132 
Non-aqueous  solutions,   137-139, 

142-151 
Number  of  atoms  hi  molecules  or 

ions,  134 

OHM'S  law,  106 

Optical  properties,  38,  50,  51,  53 
Organic  chemistry,  16 
Organic  ions,  45 
"Osiris,"  3 

Osmotic  pressure,  7, 74,  77,  85,  86, 
98,  162.  170,  175-179, 197 


246 


INDEX  OF  SUBJECTS. 


Ostwald's  law,  111,  169,  198 

rule,  135 
Oxidation,  stages  of,  18 

PALLADIUM,  49 
Partial  pressure,  154 

reactions,  120-123 
Partition    between    phases,     87, 
153-157 

between  acids,  167 
Pepsin,  116,  119,  129 
Peptization,  119 
Peptones,  161 
Peroxide  of  hydrogen,  46 
Phlogiston  theory,  6 
Phosphorus,  28,  29,  40 
Phosphoric  acid,  210 
Photochemical  processes,  116, 127, 

128 

Physical  processes,  10-14 
Platinum,  46-49 

sponge,  122 
Poisons, 

Polarization,  electric,  108 
Polonium,  34 
Polybasic  acids,  158 
Polyvalent  ions,  42-45,  141 
Pores,  5,  6 
Precipitate,  4,  9,  43-54,  76,  77, 

104,  129 
Precipitin,  129 
Pressure,  49,  69 

influence  on  dissociation,  183 
Prime  matter,  1,  3 
Protamine,  161 
Pseudoforms,  169 
Pyridine,  170 

QUANTITATIVE  methods,  xix,  17, 

19,20 
Quantity  of  matter,  17 

RADICALS,  15,  91,  98-100 
Radioactive  changes,  121, 126, 127 

substances,  33 
Radium,  25,  30 
Raffinose,  188 
Refractive  index,  95,  190 
Rennet,  129 
Repulsive  forces,  7,  74 
Residual  current,  107 
Resorcine,  188 
Rontgen  rays,  26,  28 
Rotation,  24,  31 

of  plane  of  polarization,  96 


SACCHAROSE,  188 

Salt  action,  43^5,  51-54, 109, 110, 

164-167,  179 
Salts,  4,  5,  111 
Saponification,  116,  125 
Saponine,  156 
Saturation,  63,  68,  71 
Schiitz's  rule,  118-120 
Scintillation,  33 
Silver,  3 
Soil,  55 
Sols,  39-55 
Solubility,  74-76,  82,  84,  87,  131, 

153,  179,  202-209 
Solution,  5, 7,  56, 91-111, 197, 198, 

202-207 
solid,  156 

Solvent,  4,  75,  134,  137-151 
Specific  heat,  200 

weight,  180 
Specificity,  157 
Sphere  of  action,  68,  69 
Strength  of  acids  and  bases,  109, 

110 
Strong  electrolytes,  conductivity, 

131-152,  172-195 
Stokes's  law,  23,  31,  195 
Stone  of  the  wise,  4 
Subsidence,  43 
Sulphur,  colloidal,  51-55 
Sulphuric  acid,  49,  166 

vapor  pressure,  81,  131,  149 
Surface  tension,  70,  91-94,  97 
Suspensions,  22,  36-54,  157,  177 

TANNING  processes,  55 

Temperature,  influence,  70,  74,  82, 
84,  86,  106,  107,  109,  112,  115, 
121,  123-129,  134,  135,  144-146 

Terpenes,  49 

Tetanolysin  129 

Tetraethyl  ammonium  iodide,  142 

Thermodynamics,  65,  72,  73,  79, 
81-84,  88,  89,  196-223 

Thermoneutrality,  96 

Tin,  3,  13 

Tiophene,  156 

Transition  point,  13 

Transmutability,  1,  2,  4 

Trimethylpyridin,  205 

Trypsin,  116,  119,  129 

Tyndall's  phenomenon,  38,  39 

ULTRAMICROSCOPE,  23,  38,  40 
Ultraviolet  light,  32,  114 
Unpolarizable  electrodes,  163 


INDEX  OF  SUBJECTS. 


247 


VACUA,  62 

Valency,  135 

Van't  Hoff's  rule,  124,  126,  129 

Vapor  pressure,  82,  87,  131,  154 

Velocity  of  reaction,  13,  46-49,  78, 

104,  110,  112-130,  165 
Vibriolysin,  129 
Viscosity,  26,  107,  163,  185 
Vital  processes,  116,  117,  129,  130 
Volume  of  dissociation,  182,  183 

of  neutralization,  182,  183 

of  reacting  gases,  20 

specific,  94-97 


WATER,  1, 2, 13, 14, 15, 17, 20, 210^ 

214,  222 

maximum  density  of,  11 
of  crystallization,  6 
retarding  processes,  121 

Wehnelt,  interrupter,  30 

YEAST,  113,  115 

ZEOLITES,  10 
Zymase,  114 


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